×

DC programming and DCA: thirty years of developments. (English) Zbl 1387.90197

Summary: The year 2015 marks the 30th birthday of DC (Difference of Convex functions) programming and DCA (DC Algorithms) which constitute the backbone of nonconvex programming and global optimization. In this article we offer a short survey on thirty years of developments of these theoretical and algorithmic tools. The survey is comprised of three parts. In the first part we present a brief history of the field, while in the second we summarize the state-of-the-art results and recent advances. We focus on main theoretical results and DCA solvers for important classes of difficult nonconvex optimization problems, and then give an overview of real-world applications whose solution methods are based on DCA. The third part is devoted to new trends and important open issues, as well as suggestions for future developments.

MSC:

90C26 Nonconvex programming, global optimization
90-02 Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming
90-03 History of operations research and mathematical programming
01A60 History of mathematics in the 20th century
01A61 History of mathematics in the 21st century
90C90 Applications of mathematical programming

Software:

spcov; CPLEX; LOQO; PSwarm
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Ahn, M., Pang, J.S., Xin, J.: Difference-of-convex learning: directional stationarity, optimality, and sparsity. SIAM J. Optim. 27(3), 1637-1665 (2017) · Zbl 1369.90130
[2] Akoa, F.B.: Combining DC algorithms (DCAs) and decomposition techniques for the training of nonpositive-semidefinite kernels. IEEE Trans. Neural Netw. 19(11), 1854-1872 (2008)
[3] Alexandroff, A.: On functions representable as a difference of convex functions. Doklady Akad. Nauk SSSR (N.S.) 72, 613-616 . [English translation: Siberian Elektron. Mathetical. Izv. 9 (2012) 360-376.] (1950) · Zbl 0054.05901
[4] Alvarado, A., Scutari, G., Pang, J.S.: A new decomposition method for multiuser dc-programming and its applications. IEEE Trans. Signal Process. 62(11), 2984-2998 (2014) · Zbl 1393.90091
[5] Argyriou, A., Hauser, R., Micchelli, C.A., Pontil, M.: A DC-programming algorithm for kernel selection. In: ICML 2006, pp. 41-48. ACM (2006)
[6] Arthanari, T.S., Le Thi, H.A.: New formulations of the multiple sequence alignment problem. Optim. Lett. 5(1), 27-40 (2011) · Zbl 1213.90176
[7] Astorino, A., Fuduli, A.: Semisupervised spherical separation. Appl. Math. Model. 39(20), 6351-6358 (2015) · Zbl 1320.90077
[8] Astorino, A., Fuduli, A., Gaudioso, M.: DC models for spherical separation. J. Global Optim. 48(4), 657-669 (2010) · Zbl 1206.90120
[9] Astorino, A., Fuduli, A., Gaudioso, M.: Margin maximization in spherical separation. Comput. Optim. Appl. 53(2), 301-322 (2012) · Zbl 1258.90066
[10] Attouch, H., Bolte, J.: On the convergence of the proximal algorithm for nonsmooth functions involving analytic features. Math. Program. 116(1), 5-16 (2009) · Zbl 1165.90018
[11] Attouch, H., Bolte, J., Svaiter, B.F.: Convergence of descent methods for semi-algebraic and tame problems: proximal algorithms, forward-backward splitting, and regularized Gauss-Seidel methods. Math. Program. 137(1), 91-129 (2013) · Zbl 1260.49048
[12] Bačák, M., Borwein, J.M.: On difference convexity of locally lipschitz functions. Optimization 60(8-9), 961-978 (2011) · Zbl 1237.46007
[13] Beck, A., Teboulle, M.: A fast iterative shrinkage-thresholding algorithm for linear inverse problems. SIAM J. Imaging Sci. 2(1), 183-202 (2009) · Zbl 1175.94009
[14] Ben-Tal, A., El Ghaoui, L., Nemirovski, A.: Robust Optimization. Princeton Series in Applied Mathematics. Princeton University Press, Princeton (2009) · Zbl 1221.90001
[15] Bertsekas, D.P.: Incremental proximal methods for large scale convex optimization. Math. Program. 129(2), 163-195 (2011) · Zbl 1229.90121
[16] Bien, J., Tibshirani, R.J.: Sparse estimation of a covariance matrix. Biometrika 98(4), 807-820 (2011) · Zbl 1228.62063
[17] Bottou, L.: On-line learning in neural networks. Chap. In: On-line Learning and Stochastic Approximations, pp. 9-42. Cambridge University Press, New York, NY, USA (1998) · Zbl 0968.68127
[18] Bouallagui, S.: Techniques d’optimisation déterministe et stochastique pour la résolution de problèmes difficiles en cryptologie. Ph.D. thesis, INSA de Rouen (2010)
[19] Bouallagui, S., Le Thi, H.A.: Pham Dinh, T.: Design of highly nonlinear balanced boolean functions using an hybridation of DCA and simulated annealing algorithm. In: Modelling, Computation and Optimization in Information Systems and Management Sciences, Communications in Computer and Information Science, vol. 14, pp. 579-588. Springer, Berlin, Heidelberg (2008) · Zbl 1160.90583
[20] Bradley, P.S., Mangasarian, O.L.: Feature selection via concave minimization and support vector machines. ICML 1998, 82-90 (1998)
[21] Candes, E.J., Wakin, M., Boyd, S.: Enhancing sparsity by reweighted-\[l_1\] l1 minimization. J. Fourier Anal. Appl. 14, 877-905 (2008) · Zbl 1176.94014
[22] Chambolle, A., Vore, R.A.D., Lee, N.Y., Lucier, B.J.: Nonlinear wavelet image processing: variational problems, compression, and noise removal through wavelet shrinkage. IEEE Trans. Image Process. 7(3), 319-335 (1998) · Zbl 0993.94507
[23] Chartrand, R., Yin, W.: Iteratively reweighted algorithms for compressive sensing. In: IEEE International Conference on Acoustics, Speech and Signal Processing, 2008, pp. 3869-3872 (2008) · Zbl 1393.94918
[24] Che, E., Tuan, H.D., Nguyen, H.H.: Joint optimization of cooperative beamforming and relay assignment in multi-user wireless relay networks. IEEE Trans. Wirel. Commun. 13(10), 5481-5495 (2014)
[25] Chen, G., Zeng, D., Kosorok, M.R.: Personalized dose finding using outcome weighted learning. J. Am. Stat. Assoc. 111(516), 1509-1521 (2016)
[26] Cheng, Y., Pesavento, M.: Joint optimization of source power allocation and distributed relay beamforming in multiuser peer-to-peer relay networks. IEEE Trans. Signal Process. 60(6), 2962-2973 (2012) · Zbl 1393.94020
[27] Cheung, P.M., Kwok, J.T.: A regularization framework for multiple-instance learning. In: ICML 2006, pp. 193-200. ACM, New York, NY, USA (2006) · Zbl 1391.90166
[28] Collobert, R., Sinz, F., Weston, J., Bottou, L.: Large scale transductive SVMs. J. Mach. Learn. Res. 7, 1687-1712 (2006) · Zbl 1222.68173
[29] Collobert, R., Sinz, F., Weston, J., Bottou, L.: Trading convexity for scalability. In: ICML 2006, pp. 201-208 (2006) · Zbl 1394.94916
[30] Combettes, P.L., Wajs, V.R.: Signal recovery by proximal forward-backward splitting. Multiscale Model. Simul. 4(4), 1168-1200 (2005) · Zbl 1179.94031
[31] Conn, A., Gould, N., Toint, P.: Trust Region Methods. SIAM, Philadelphia (2000) · Zbl 0958.65071
[32] Daubechies, I., Defrise, M., De Mol, C.: An iterative thresholding algorithm for linear inverse problems with a sparsity constraint. Commun. Pure Appl. Math. 57(11), 1413-1457 (2004) · Zbl 1077.65055
[33] Dempster, A.P., Laird, N.M., Rubin, D.B.: Maximum likelihood from incomplete data via the EM algorithm. J. R. Stat. Soc. B Methodol. 39(1), 1-38 (1977) · Zbl 0364.62022
[34] El Azami, M., Lartizien, C., Canu, S.: Robust outlier detection with L0-SVDD. In: European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning, ESANN 2014, pp. 389-394 (2014) · Zbl 1393.94918
[35] Ellis, S.E., Nayakkankuppam, M.V.: Phylogenetic analysis via DC programming . (Preprint) (2003)
[36] Esser, E., Lou, Y., Xin, J.: A method for finding structured sparse solutions to nonnegative least squares problems with applications. SIAM J. Imaging Sci. 6(4), 2010-2046 (2013) · Zbl 1282.90239
[37] Fan, J., Li, R.: Variable selection via nonconcave penalized likelihood and its oracle properties. J. Am. Stat. Assoc. 96(456), 1348-1360 (2001) · Zbl 1073.62547
[38] Fastrich, B., Paterlini, S., Winker, P.: Constructing optimal sparse portfolios using regularization methods. CMS 12(3), 417-434 (2015) · Zbl 1355.91077
[39] Fawzi, A., Davies, M., Frossard, P.: Dictionary learning for fast classification based on soft-thresholding. Int. J. Comput. Vis. 114(2), 306-321 (2015) · Zbl 1398.94030
[40] Feng, D., Yu, G., Yuan-Wu, Y., Li, G.Y., Feng, G., Li, S.: Mode switching for energy-efficient device-to-device communications in cellular networks. IEEE Trans. Wirel. Commun. 14(12), 6993-7003 (2015)
[41] Floudas, C.A., Pardalos, P.M., Adjiman, C., Esposito, W.R., Gümüs, Z.H., Harding, S.T., Klepeis, J.L., Meyer, C.A., Schweiger, C.A.: Handbook of test problems in local and global optimization. In: Nonconvex Optimization and Its Applications, vol. 33. Springer, USA (1999) · Zbl 0943.90001
[42] Gasso, G., Pappaioannou, A., Spivak, M., Bottou, L.: Batch and online learning algorithms for nonconvex Neyman-Pearson classification. ACM Trans. Intell. Syst. Technol. 2(3), 28:1-28:19 (2011)
[43] Gasso, G., Rakotomamonjy, A., Canu, S.: Recovering sparse signals with a certain family of nonconvex penalties and DC programming. IEEE Trans. Signal Process. 57(12), 4686-4698 (2009) · Zbl 1391.90489
[44] Geng, J., Wang, L., Wang, Y.: A non-convex algorithm framework based on DC programming and DCA for matrix completion. Numer. Algorithms 68(4), 903-921 (2015) · Zbl 1312.65093
[45] Gholami, M.R., Gezici, S., Strom, E.G.: A concave-convex procedure for TDOA based positioning. IEEE Commun. Lett. 17(4), 765-768 (2013)
[46] Göernitz, N., Braun, M., Kloft, M.: Hidden Markov anomaly detection. In: Proceedings of the 32nd International Conference on Machine Learning, vol. 37, pp. 1833-1842. JMLR: W&CP (2015)
[47] Gong, P., Zhang, C., Lu, Z., Huang, J.Z., Ye, J.: A general iterative shrinkage and thresholding algorithm for non-convex regularized optimization problems. In: Proceedings of the 30th International Conference on International Conference on Machine Learning, ICML’13, vol. 28, pp. II-37-II-45 (2013) · Zbl 1226.90060
[48] Gorodnitsky, I.F., Rao, B.D.: Sparse signal reconstructions from limited data using FOCUSS: a re-weighted minimum norm algorithm. IEEE Trans. Signal Process. 45(3), 600-616 (1997)
[49] Guan, G., Gray, A.: Sparse high-dimensional fractional-norm support vector machine via DC programming. Comput. Stat. Data Anal. 67, 136-148 (2013) · Zbl 1471.62080
[50] Gülpinar, N., Le Thi, H.A., Moeini, M.: Robust investment strategies with discrete asset choice constraints using DC programming and DCA. Optimization 59(1), 45-62 (2010) · Zbl 1188.90184
[51] Hale, E.T., Yin, W., Zhang, Y.: Fixed-point continuation for \[\ell_1\] ℓ1-minimization: methodology and convergence. SIAM J. Optim. 19(3), 1107-1130 (2008) · Zbl 1180.65076
[52] Hartman, P.: On functions representable as a difference of convex functions. Pac. J. Math. 9(3), 707-713 (1959) · Zbl 0093.06401
[53] Heinkenschloss, M.: On the solution of a two ball trust region subproblem. Math. Program. 64(1-3), 249-276 (1994) · Zbl 0819.90067
[54] Hiriart-Urruty, J.B.: From Convex Optimization to Nonconvex Optimization. Part I Necessary and Sufficient Conditions for Global Optimality, pp. 219-239. Springer, Boston (1989) · Zbl 0735.90056
[55] Ho, V.T.: Advanced machine learning techniques based on DC programming and DCA. Ph.D. thesis, University of Lorraine (2017) · Zbl 0876.90071
[56] Ho, VT; Thi, HA; Nguyen, TB (ed.); Do, T. (ed.); Thi, HA (ed.); Nguyen, NT (ed.), Solving an infinite-horizon discounted Markov decision process by DC programming and DCA, 43-55 (2016), Berlin · Zbl 1358.90148
[57] Ho, VT; Thi, HA; Bui, DC; Nguyen, TN (ed.); Trawiński, B. (ed.); Fujita, H. (ed.); Hong, TP (ed.), Online DC optimization for online binary linear classification, 661-670 (2016), Berlin
[58] Hong, M., Razaviyayn, M., Luo, Z.Q., Pang, J.S.: A unified algorithmic framework for block-structured optimization involving big data: with applications in machine learning and signal processing. IEEE Signal Process. Mag. 33(1), 57-77 (2016)
[59] Huang, X., Shi, L., Suykens, J.: Ramp loss linear programming support vector machine. J. Mach. Learn. Res. 15(1), 2185-2211 (2014) · Zbl 1318.68144
[60] Hunter, D.R., Lange, K.: Rejoinder to discussion of optimization transfer using surrogate objective functions. Comput. Graph. Stat. 9, 52-59 (2000)
[61] IBM: CPLEX Optimizer. https://www.ibm.com/analytics/data-science/prescriptive-analytics/cplex-optimizer · Zbl 1282.91313
[62] Jara-Moroni, F., Pang, J.S., Waechter, A.: A study of the difference-of-convex approach for solving linear programs with complementarity constraints. Math. Program. Ser. B (2018, to appear) · Zbl 1397.90264
[63] Jeong, S., Simeone, O., Haimovich, A., Kang, J.: Optimal fronthaul quantization for cloud radio positioning. IEEE Trans. Veh. Technol. 65(4), 2763-2768 (2016)
[64] Júdice, J.J., Sherali, H.D., Ribeiro, I.M.: The eigenvalue complementarity problem. Comput. Optim. Appl. 37(2), 139-156 (2007) · Zbl 1181.90261
[65] Júdice, J.J., Sherali, H.D., Ribeiro, I.M., Rosa, S.S.: On the asymmetric eigenvalue complementarity problem. Optim. Methods Softw. 24(4-5), 549-568 (2009) · Zbl 1177.90386
[66] Kaplan, A., Tichatschke, R.: Proximal point methods and nonconvex optimization. J. Global Optim. 13(4), 389-406 (1998) · Zbl 0916.90224
[67] Khalaf, W., Astorino, A., D’Alessandro, P., Gaudioso, M.: A DC optimization-based clustering technique for edge detection. Optim. Lett. 11(3), 627-640 (2017) · Zbl 1366.90170
[68] Kim, S., Pan, W., Shen, X.: Network-based penalized regression with application to genomic data. Biometrics 69(3), 582-93 (2013) · Zbl 1429.62294
[69] Krause, N., Singer, Y.: Leveraging the margin more carefully. In: Proceedings of the twenty-first international conference on Machine learning ICML 2004, p. 63 (2004) · Zbl 1307.90145
[70] Krummenacher, G., Ong, C.S., Buhmann, J.: Ellipsoidal multiple instance learning. In: Dasgupta, S., Mcallester, D. (eds.) ICML 2013, JMLR: W&CP, vol. 28, pp. 73-81 (2013)
[71] Kuang, Q., Speidel, J., Droste, H.: Joint base-station association, channel assignment, beamforming and power control in heterogeneous networks. In: IEEE 75th Vehicular Technology Conference (VTC Spring), pp. 1-5 (2012)
[72] Kwon, S., Ahn, J., Jang, W., Lee, S., Kim, Y.: A doubly sparse approach for group variable selection. Ann. Inst. Stat. Math. 69(5), 997-1025 (2017) · Zbl 1436.62327
[73] Laporte, L., Flamary, R., Canu, S., Déjean, S., Mothe, J.: Nonconvex regularizations for feature selection in ranking with sparse SVM. IEEE Trans. Neural Netw. Learn. 25(6), 1118-1130 (2014)
[74] Le, AV; Thi, HA; Nguyen, MC; Zidna, A.; Nguyen, NT (ed.); Hoang, K. (ed.); Jedrzejowicz, P. (ed.), Network intrusion detection based on multi-class support vector machine, 536-543 (2012), Berlin
[75] Le, H.M.: Modélisation et optimisation non convexe basées sur la programmation DC et DCA pour la résolution de certaines classes des problémes en fouille de données et cryptologie. Ph.D. thesis, Université Paul Verlaine-Metz (2007) · Zbl 1364.90266
[76] Le, H.M., Le Thi, H.A., Nguyen, M.C.: Sparse semi-supervised support vector machines by DC programming and DCA. Neurocomputing 153, 62-76 (2015)
[77] Le, H.M., Le Thi, H.A., Pham Dinh, T., Bouvry, P.: A combined DCA: GA for constructing highly nonlinear balanced boolean functions in cryptography. J. Global Optim. 47(4), 597-613 (2010) · Zbl 1229.90091
[78] Le, H.M., Le Thi, H.A., Pham Dinh, T., Huynh, V.N.: Block clustering based on Difference of Convex functions (DC) programming and DC algorithms. Neural Comput. 25(10), 2776-2807 (2013) · Zbl 1418.62253
[79] Le, H.M., Nguyen, T.B.T., Ta, M.T., Le Thi, H.A.: Image segmentation via feature weighted fuzzy clustering by a DCA based algorithm. In: Advanced Computational Methods for Knowledge Engineering, Studies in Computational Intelligence, vol. 479, pp. 53-63. Springer (2013) · Zbl 1281.62106
[80] Le, H.M., Ta, M.T.: DC programming and DCA for solving minimum sum-of-squares clustering using weighted dissimilarity measures. In: Transactions on Computational Intelligence XIII, LNCS, vol. 8342, pp. 113-131. Springer, Berlin, Heidelberg (2014)
[81] Le, H.M., Yassine, A., Moussi, R.: DCA for solving the scheduling of lifting vehicle in an automated port container terminal. Comput. Manag. Sci. 9(2), 273-286 (2012) · Zbl 1273.90161
[82] Le Thi, H.A.: Analyse numérique des algorithmes de l’optimisation DC. Approches locale et globale. Codes et simulations numériques en grande dimension. Applications. Ph.D. thesis, Université de Rouen (1994)
[83] Le Thi, H.A.: Contribution à l’optimisation non convexe et l’optimisation globale: : Théorie. Algorithmes et Applications. Habilitation à Diriger des Recherches, National Institute for Applied Sciences, Rouen (1997)
[84] Le Thi, H.A.: An efficient algorithm for globally minimizing a quadratic function under convex quadratic constraints. Math. Program. 87(3), 401-426 (2000) · Zbl 0952.90031
[85] Le Thi, H.A.: Solving large scale molecular distance geometry problems by a smoothing technique via the Gaussian transform and D.C. programming. J. Global Optim. 27(4), 375-397 (2003) · Zbl 1064.90036
[86] Le Thi, H.A.: DCA collaborative for clustering. University of Lorraine, Tech. rep. (2013)
[87] Le Thi, H.A.: Phylogenetic tree reconstruction by a DCA based algorithm. Tech. rep., LITA, University of Lorraine (2013)
[88] Thi, HA; Adamatzky, A. (ed.), DC programming and DCA for challenging problems in bioinformatics and computational biology, No. 12, 383-414 (2015), Berlin · Zbl 1309.90079
[89] Le Thi, H.A., Belghiti, M.T., Pham Dinh, T.: A new efficient algorithm based on DC programming and DCA for clustering. J. Global Optim. 37(4), 593-608 (2007) · Zbl 1198.90327
[90] Le Thi, H.A., Ho, V.T.: Online learning based on Online DCA (2016, Submitted) · Zbl 1468.68157
[91] Thi, HA; Huynh, VN; Pham Dinh, T.; Do, T. (ed.); Thi, HA (ed.); Nguyen, NT (ed.), DC programming and DCA for general DC programs, 15-35 (2014), Berlin · Zbl 1322.90072
[92] Le Thi, H.A., Huynh, V.N., Pham Dinh, T.: Error bounds via exact penalization with applications to concave and quadratic systems. J. Optim. Theory Appl. 171(1), 228-250 (2016) · Zbl 1353.49020
[93] Le Thi, H.A., Huynh, V.N., Pham Dinh, T.: Convergence analysis of DCA with subanalytic data. J. Optim. Theory Appl. (2018) · Zbl 1409.90187
[94] Le Thi, H.A., Huynh, V.N., Pham Dinh, T., Vaz, A.I.F., Vicente, L.N.: Globally convergent DC trust-region methods. J. Global Optim. 59(2), 209-225 (2014) · Zbl 1300.90029
[95] Le Thi, H.A., Le, H.M., Nguyen, T.P., Pham Dinh, T.: Noisy image segmentation by a robust clustering algorithm based on DC programming and DCA. In: Proceedings of the 8th Industrial Conference on Advances in Data Mining, ICDM’08, pp. 72-86. Springer (2008)
[96] Le Thi, H.A., Le, H.M., Nguyen, V.V., Pham Dinh, T.: A DC programming approach for feature selection in support vector machines learning. Adv. Data Anal. Classif. 2(3), 259-278 (2008) · Zbl 1284.90057
[97] Le Thi, H.A., Le, H.M., Pham Dinh, T.: Fuzzy clustering based on nonconvex optimisation approaches using difference of convex (DC) functions algorithms. Adv. Data Anal. Classif. 1(2), 85-104 (2007) · Zbl 1301.90072
[98] Le Thi, H.A., Le, H.M., Pham Dinh, T.: New and efficient DCA based algorithms for minimum sum-of-squares clustering. Pattern Recognit. 47(1), 388-401 (2014) · Zbl 1326.68225
[99] Le Thi, H.A., Le, H.M., Pham Dinh, T.: Feature selection in machine learning: an exact penalty approach using a difference of convex function algorithm. Mach. Learn. 101(1-3), 163-186 (2015) · Zbl 1343.68201
[100] Le Thi, H.A., Le, H.M., Pham Dinh, T., Bouvry, P.: Solving the perceptron problem by deterministic optimization approach based on DC programming and DCA. In: INDIN 2009, Cardiff. IEEE (2009) · Zbl 1235.68203
[101] Le Thi, H.A., Le, H.M., Pham Dinh, T., Huynh, V.N.: Binary classification via spherical separator by DC programming and DCA. J. Global Optim. 56(4), 1393-1407 (2013) · Zbl 1275.90093
[102] Le Thi, H.A., Le, H.M., Phan, D.N., Tran, B.: Stochastic DCA for the large-sum of non-convex functions problem and its application to group variable selection in classification. In: Proceedings of the 34th International Conference on Machine Learning, ICML 2017, Sydney, NSW, Australia, 6-11 August 2017, pp. 3394-3403 (2017)
[103] Le Thi, H.A., Le, : M.T., Nguyen, T.B.T.: A novel approach to automated cell counting based on a difference of convex functions algorithm (DCA). In: Computational Collective Intelligence. Technologies and Applications, LNCS, vol. 8083, pp. 336-345. Springer, Berlin, Heidelberg (2013) · Zbl 06195973
[104] Le Thi, H.A., Moeini, M.: Long-short portfolio optimization under cardinality constraints by difference of convex functions algorithm. J. Optim. Theory Appl. 161(1), 199-224 (2014) · Zbl 1300.91046
[105] Le Thi, H.A., Moeini, M., Pham Dinh, T.: DC programming approach for portfolio optimization under step increasing transaction costs. Optimization 58(3), 267-289 (2009) · Zbl 1160.91015
[106] Le Thi, H.A., Moeini, M., Pham Dinh, T.: Portfolio selection under downside risk measures and cardinality constraints based on DC programming and DCA. Comput. Manag. Sci. 6(4), 459-475 (2009) · Zbl 1188.90185
[107] Le Thi, H.A., Moeini, M., Pham Dinh, T., Joaquim, J.: A DC programming approach for solving the symmetric eigenvalue complementarity problem. Comput. Optim. Appl. 51(3), 1097-1117 (2012) · Zbl 1241.90153
[108] Le Thi, H.A., Ndiaye, B.M., Pham Dinh, T.: Solving a multimodal transport problem by DCA. In: IEEE International Conference on Research, Innovation and Vision for the Future, pp. 49-56 (2008)
[109] Le Thi, H.A., Nguyen, D.M., Pham Dinh, T.: A DC programming approach for planning a multisensor multizone search for a target. Comput. Oper. Res. 41, 231-239 (2014) · Zbl 1348.90347
[110] Le Thi, H.A., Nguyen, M.C.: Self-organizing maps by difference of convex functions optimization. Data Min. Knowl. Disc. 28(5-6), 1336-1365 (2014) · Zbl 1342.90147
[111] Le Thi, H.A., Nguyen, M.C.: DCA based algorithms for feature selection in multi-class support vector machine. Ann. Oper. Res. 249(1), 273-300 (2017) · Zbl 1404.68111
[112] Le Thi, H.A., Nguyen, M.C., Pham Dinh, T.: A DC programming approach for finding communities in networks. Neural Comput. 26(12), 2827-2854 (2014) · Zbl 1415.68168
[113] Le Thi, H.A., Nguyen, Q.T.: A robust approach for nonlinear UAV task assignment problem under uncertainty. Transactions on Computational Collective Intelligence II. LNCS, vol. 6450, pp. 147-159. Springer, Berlin, Heidelberg (2010) · Zbl 1242.90095
[114] Le Thi, H.A., Nguyen, Q.T., Nguyen, H.T., Pham Dinh, T.: Solving the earliness tardiness scheduling problem by DC programming and DCA. Math. Balk. 23(3-4), 271-288 (2009) · Zbl 1192.90081
[115] Le Thi, H.A., Nguyen, Q.T., Nguyen, H.T., Pham Dinh, T.: A time-indexed formulation of earliness tardiness scheduling via DC programming and DCA. In: International Multiconference on Computer Science and Information Technology IMCSIT’09, pp. 2009 (779-784) · Zbl 0531.65022
[116] Le Thi, H.A., Nguyen, Q.T., Phan, K.T., Pham Dinh, T.: Energy minimization-based cross-layer design in wireless networks. In: Proceedings of the 2008 High Performance Computing & Simulation Conference (HPCS 2008), pp. 283-289 (2008) · Zbl 1393.90091
[117] Le Thi, H.A., Nguyen, Q.T., Phan, K.T., Pham Dinh, T.: DC programming and DCA based cross-layer optimization in multi-hop TDMA networks. Intelligent Information and Database Systems. LNCS, vol. 7803, pp. 398-408. Springer, Berlin, Heidelberg (2013) · Zbl 1119.62341
[118] Le Thi, H.A., Nguyen, T.B.T., Le, : H.M.: Sparse signal recovery by difference of convex functions algorithms. In; Intelligent Information and Database Systems. LNCS, vol. 7803, pp. 387-397. Springer, Berlin, Heidelberg (2013)
[119] Le Thi, H.A., Nguyen, T.P., Pham Dinh, T.: A continuous DC programming approach to the strategic supply chain design problem from qualified partner set. Eur. J. Oper. Res. 183(3), 1001-1012 (2007) · Zbl 1135.90036
[120] Le Thi, H.A., Nguyen, V.V., Ouchani, S.: Gene selection for cancer classification using DCA. J. Front. Comput. Sci. Technol. 3(6), 612-620 (2009)
[121] Le Thi, H.A., Pham Dinh, T.: Solving a class of linearly constrained indefinite quadratic problems by D.C. algorithms. J. Global Optim. 11(3), 253-285 (1997) · Zbl 0905.90131
[122] Le Thi, H.A., Pham Dinh, T.: A branch-and-bound method via D.C. optimization algorithm and ellipsoidal technique for box constrained nonconvex quadratic programming problems. J. Global Optim. 13(2), 171-206 (1998) · Zbl 0912.90233
[123] Thi, HA; Pham Dinh, T.; Floudas, CA (ed.); Pardalos, PM (ed.), D.C. programming approach for large-scale molecular optimization via the general distance geometry problem, No. 40, 301-339 (2000), New York
[124] Le Thi, H.A., Pham Dinh, T.: A continuous approach for globally solving linearly constrained quadratic zero-one programming problems. Optimization 50(1-2), 93-120 (2001) · Zbl 1039.90050
[125] Thi, HA; Pham Dinh, T.; Hadjisavvas, N. (ed.); Pardalos, P. (ed.), D.C. optimization approaches via Markov models for restoration of signal (1-D) and (2-D), 303-317 (2001), Dordrecht · Zbl 1049.90065
[126] Thi, HA; Pham Dinh, T.; Migdalas, A. (ed.); Pardalos, PM (ed.); Värbrand, P. (ed.), D.C. programming approach to the multidimensional scaling problem, 231-276 (2001), New York
[127] Le Thi, H.A., Pham Dinh, T.: D.C. programming approach for multicommodity network optimization problems with step increasing cost functions. J. Global Optim. 22(1), 205-232 (2002) · Zbl 1045.90074
[128] Le Thi, H.A., Pham Dinh, T.: Large scale molecular optimization from distance matrices by a D.C. optimization approach. SIAM J. Optim. 14(1), 77-114 (2003) · Zbl 1075.90071
[129] Thi, HA; Pham Dinh, T.; Pillo, G. (ed.); Murli, A. (ed.), A new algorithm for solving large scale molecular distance geometry problems, No. 82, 285-302 (2003), New York · Zbl 1112.90367
[130] Le Thi, H.A., Pham Dinh, T.: The DC (difference of convex functions) programming and DCA revisited with DC models of real world nonconvex optimization problems. Ann. Oper. Res. 133(1-4), 23-48 (2005) · Zbl 1116.90122
[131] Le Thi, H.A., Pham Dinh, T.: A continuous approach for the concave cost supply problem via DC programming and DCA. Discrete Appl. Math. 156(3), 325-338 (2008) · Zbl 1190.90142
[132] Le Thi, H.A., Pham Dinh, T.: On solving linear complemetarity problems by DC programming and DCA. Comput. Optim. Appl. 50(3), 507-524 (2011) · Zbl 1237.90234
[133] Le Thi, H.A., Pham Dinh, T.: A two phases DCA based algorithm for solving the Lennard-Jones problem. Tech. rep., LITA, University of Metz (2011) · Zbl 1436.62327
[134] Le Thi, H.A., Pham Dinh, T.: Minimizing the morse potential energy function by a DC programming approach. Tech. rep., LITA, University of Lorraine (2012) · Zbl 1044.90071
[135] Thi, HA; Pham Dinh, T.; Mucherino, A. (ed.); Lavor, C. (ed.); Liberti, L. (ed.); Maculan, N. (ed.), DC programming approaches for distance geometry problems, 225-290 (2013), New York
[136] Le Thi, H.A., Pham Dinh, T.: Network utility maximisation: A DC programming approach for Sigmoidal utility function. In: International Conference on Advanced Technologies for Communications (ATC’13), pp. 50-54 (2013) · Zbl 1394.94916
[137] Le Thi, H.A., Pham Dinh, T.: DC programming in communication systems: challenging problems and methods. Vietnam J. Comput. Sci. 1(1), 15-28 (2014)
[138] Le Thi, H.A., Pham Dinh, T.: Difference of convex functions algorithms (DCA) for image restoration via a Markov random field model. Optim. Eng. 18(4), 873-906 (2017) · Zbl 1390.90624
[139] Le Thi, H.A., Pham Dinh, T., Belghiti, M.: DCA based algorithms for multiple sequence alignment (MSA). Cent. Eur. J. Oper. Res. 22(3), 501-524 (2014) · Zbl 1339.92064
[140] Le Thi, H.A., Pham Dinh, T., Bouallagui, S.: Cryptanalysis of an identification scheme based on the perceptron problem using a hybridization of deterministic optimization and genetic algorithm. In: Proceedings of the 2009 International Conference on Security & Management, SAM 2009, pp. 117-123. CSREA Press (2009) · Zbl 1242.49037
[141] Le Thi, H.A., Pham Dinh, T., Huynh, V.N.: Exact penalty techniques in DC programming. Tech. rep, National Institute for Applied Sciences, Rouen (2005) · Zbl 1242.49037
[142] Le Thi, H.A., Pham Dinh, T., Huynh, V.N.: Optimization based DC programming and DCA for hierarchical clustering. Eur. J. Oper. Res. 183(3), 1067-1085 (2007) · Zbl 1149.90117
[143] Le Thi, H.A., Pham Dinh, T., Huynh, V.N.: Exact penalty and error bounds in DC programming. J. Global Optim. 52(3), 509-535 (2012) · Zbl 1242.49037
[144] Le Thi, H.A., Pham Dinh, T., Le, H.M., Vo, X.T.: DC approximation approaches for sparse optimization. Eur. J. Oper. Res. 244(1), 26-46 (2015) · Zbl 1346.90819
[145] Le Thi, H.A., Pham Dinh, T., Muu, L.D.: Numerical solution for optimization over the efficient set by D.C. optimization algorithm. Oper. Res. Lett. 19(3), 117-128 (1996) · Zbl 0871.90074
[146] Le Thi, H.A., Pham Dinh, T., Muu, L.D.: A combined D.C. optimization-ellipsoidal branch-and-bound algorithm for solving nonconvex quadratic programming problems. J. Comb. Optim. 2(1), 9-28 (1998) · Zbl 0904.90134
[147] Le Thi, H.A., Pham Dinh, T., Muu, L.D.: Exact penalty in DC programming. Vietnam J. Math. 27(2), 169-179 (1999) · Zbl 1006.90062
[148] Le Thi, H.A., Pham Dinh, T., Muu, L.D.: Simplicially constrained D.C. optimization over the efficient and weakly efficient sets. J. Optim. Theory Appl. 117(3), 503-521 (2003) · Zbl 1044.90071
[149] Le Thi, H.A., Pham Dinh, T., Thiao, M.: Efficient approaches for \[\ell_2-\ell_0\] ℓ2-ℓ0 regularization and applications to feature selection in SVM. Appl. Intell. 45(2), 549-565 (2016)
[150] Le Thi, H.A., Pham Dinh, T., Thoai, N.V.: Combination between global and local methods for solving an optimization problem over the efficient set. Eur. J. Oper. Res. 142(2), 258-270 (2002) · Zbl 1082.90563
[151] Le Thi, H.A., Pham Dinh, T., Thoai, N.V., Nguyen Canh, N.: D.C. optimization techniques for solving a class of nonlinear bilevel programs. J. Global Optim. 44(3), 313-337 (2009) · Zbl 1180.90241
[152] Le Thi, H.A., Pham Dinh, T., Tran, D.Q.: A DC programming approach for a class of bilevel programming problems and its application in portfolio selection. NACO Numer. Algebra Control Optim. 2(1), 167-185 (2012) · Zbl 1254.90175
[153] Le Thi, H.A., Pham Dinh, T., Yen, N.D.: Behavior of DCA sequences for solving the trust-region subproblem. J. Global Optim. 53, 317-329 (2012) · Zbl 1259.65092
[154] Le Thi, H.A., Phan, D.N.: DC programming and DCA for sparse optimal scoring problem. Neurocomputing 186, 170-181 (2016)
[155] Le Thi, H.A., Phan, D.N.: Efficient nonconvex group variable selection and application to group sparse optimal scoring (2017, Submitted) · Zbl 0848.49022
[156] Le Thi, H.A., Phan, D.N.: DC programming and DCA for sparse Fisher linear discriminant analysis. Neural Comput. Appl. 28(9), 2809-2822 (2017)
[157] Le Thi, H.A., Ta, A.S., Pham Dinh, T.: An efficient DCA based algorithm for power control in large scale wireless networks. Appl. Math. Comput. 318, 215-226 (2018) · Zbl 1426.68012
[158] Le Thi, H.A., Tran, D.Q.: Solving continuous min max problem for single period portfolio selection with discrete constraints by DCA. Optimization 61(8), 1025-1038 (2012) · Zbl 1252.90067
[159] Le Thi, H.A., Tran, D.Q.: New and efficient algorithms for transfer prices and inventory holding policies in two-enterprise supply chains. J. Global Optim. 60(1), 5-24 (2014) · Zbl 1304.90164
[160] Le Thi, H.A., Tran, D.Q.: Optimizing a multi-stage production/inventory system by DC programming based approaches. Comput. Optim. Appl. 57(2), 441-468 (2014) · Zbl 1330.90055
[161] Le Thi, H.A., Tran, Q.D., Adjallah, K.H.: A difference of convex functions algorithm for optimal scheduling and real-time assignment of preventive maintenance jobs on parallel processors. J. Ind. Manag. Optim. 10(1), 243-258 (2014) · Zbl 1281.90029
[162] Thi, HA; Tran, TT; Pham Dinh, T.; Gély, A.; Nguyen, TB (ed.); Do, T. (ed.); Thi, HA (ed.); Nguyen, NT (ed.), DC programming and DCA for transmit beamforming and power allocation in multicasting relay network, 29-41 (2016), New York · Zbl 1358.90106
[163] Le Thi, H.A., Vaz, A.I.F., Vicente, L.N.: Optimizing radial basis functions by D.C. programming and its use in direct search for global derivative-free optimization. TOP 20(1), 190-214 (2012) · Zbl 1267.90110
[164] Le Thi, H.A., Vo, X.T., Pham Dinh, T.: Feature selection for linear SVMs under uncertain data: robust optimization based on difference of convex functions algorithms. Neural Netw. 59, 36-50 (2014) · Zbl 1327.90236
[165] Le Thi, H.A., Vo, X.T., Pham Dinh, T.: Efficient nonegative matrix factorization by DC programming and DCA. Neural Comput. 28(6), 1163-1216 (2016) · Zbl 1472.65070
[166] Le Thi, H.A.: DC Programming and DCA: http://www.lita.univ-lorraine.fr/ lethi/index.php/en/research/dc-programming-and-dca.html (Homepage) (2005) · Zbl 1116.90122
[167] Lee, J.D., Sun, Y., Saunders, M.A.: Proximal newton-type methods for minimizing composite functions. SIAM J. Optim. 24(3), 1420-1443 (2014) · Zbl 1306.65213
[168] Leeuw, J.; Barra, JR (ed.); Brodeau, F. (ed.); Romier, G. (ed.); Cutsem, B. (ed.), Applications of convex analysis to multidimensional scaling, 133-146 (1977), Amsterdam · Zbl 0349.00013
[169] Li, P., Rangapuram, S.S., Slawski, M.: Methods for sparse and low-rank recovery under simplex constraints. arXiv:1605.00507 (2016) · Zbl 1439.62138
[170] Li, Z., Lou, Y., Zeng, T.: Variational multiplicative noise removal by DC programming. J. Sci. Comput. 68(3), 1200-1216 (2016) · Zbl 1350.49047
[171] Liu, D., Shi, Y., Tian, Y., Huang, X.: Ramp loss least squares support vector machine. J. Comput. Sci. 14, 61-68 (2016)
[172] Liu, D., Tian, Y., Shi, Y.: Ramp loss nonparallel support vector machine for pattern classification. Knowl. Based Syst. 85, 224-233 (2015)
[173] Liu, Y., Shen, X.: Multicategory \[\psi\] ψ-learning. J. Am. Stat. Assoc. 101, 500-509 (2006) · Zbl 1119.62341
[174] Liu, Y., Shen, X., Doss, H.: Multicategory \[\psi\] ψ-learning and support vector machine: computational tools. J. Comput. Graph. Stat. 14, 219-236 (2005)
[175] Liu, Z.: Non-dominated set of a multi-objective optimisation problem. Ph.D. thesis, Lancaster University (2016) · Zbl 1180.65076
[176] Lou, Y.; Osher, S.; Xin, J.; Le Thi, HA (ed.); Pham Dinh, T. (ed.); Nguyen, NT (ed.), Computational aspects of constrained L1-L2 minimization for compressive sensing, 169-180 (2015), New York
[177] Lou, Y., Yin, P., He, Q., Xin, J.: Computing sparse representation in a highly coherent dictionary based on difference of L1 and L2. J. Sci. Comput. 64(1), 178-196 (2015) · Zbl 1327.65111
[178] Lou, Y., Yin, P., Xin, J.: Point source super-resolution via non-convex \[l_1\] l1 based methods. J. Sci. Comput. 68(3), 1082-1100 (2016) · Zbl 1354.65125
[179] Lou, Y., Zeng, T., Osher, S., Xin, J.: A weighted difference of anisotropic and isotropic total variation model for image processing. SIAM J. Imaging Sci. 8(3), 1798-1823 (2015) · Zbl 1322.94019
[180] Mahey, P., Phong, T.Q., Luna, H.P.L.: Separable convexification and DCA techniques for capacity and flow assignment problems. RAIRO Oper. Res. 35, 269-281 (2001) · Zbl 1048.90047
[181] Mangasarian, OL; Fischer, H. (ed.); Riedmueller, B. (ed.); Schaeffler, S. (ed.), Machine learning via polyhedral concave minimization, 175-188 (1996), Germany · Zbl 0906.68127
[182] Martinet, B.: Brève communication. régularisation d’inéquations variationnelles par approximations successives. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique 4(R3), 154-158 (1970) · Zbl 0215.21103
[183] Mokhtari, A., Koppel, A., Scutari, G., Ribeiro, A.: Large-scale nonconvex stochastic optimization by doubly stochastic successive convex approximation. In: 2017 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 4701-4705 (2017)
[184] Mu, P., Hu, X., Wang, B., Li, Z.: Secrecy rate maximization with uncoordinated cooperative jamming by single-antenna helpers under secrecy outage probability constraint. IEEE Commun. Lett. 19(12), 2174-2177 (2015)
[185] Ndiaye, B.M.: Simulation et optimisation DC dans les réseaux de transport combinés : codes à usage industriel. Ph.D. thesis, INSA de Rouen (2007) · Zbl 1166.62012
[186] Ndiaye, B.M., Le Thi, H.A., Pham Dinh, T.: Single straddle carrier routing problem in port container terminals: Mathematical model and solving approaches. Int. J. Intell. Inf. Database Syst. 6(6), 532-554 (2012) · Zbl 1160.90625
[187] Ndiaye, B.M., Le Thi, H.A., Pham Dinh, T., Niu, Y.: DC programming and DCA for large-scale two-dimensional packing problems. In: Intelligent Information and Database Systems. LNCS, vol. 7197, pp. 321-330. Springer, Berlin Heidelberg (2012)
[188] Ndiaye, B.M., Pham Dinh, T., Le Thi, H.A.: Single straddle carrier routing problem in port container terminals: Mathematical model and solving approaches. In: Le Thi, H.A., Bouvry, P., Pham Dinh, T. (eds.) Modelling, Computation and Optimization in Information Systems and Management Sciences, pp. 21-31 (2008) · Zbl 1160.90625
[189] Neumann, J., Schnörr, C., Steidl, G.: Combined SVM-based feature selection and classification. Mach. Learn. 61(1-3), 129-150 (2005) · Zbl 1137.90643
[190] Nguyen, D.M.: The DC programming and the cross- entropy method for some classes of problems in finance, assignment and search theory. Ph.D. thesis, INSA de Rouen (2012) · Zbl 0364.62022
[191] Nguyen, M.C.: La programmation DC et DCA pour certaines classes de problèmes en apprentissage et fouille de données. Ph.D. thesis, University of Lorraine (2014)
[192] Nguyen, Q.T.: Approches locales et globales basées sur la programmation DC et DCA pour des problèmes combinatoires en variables mixtes 0-1 : applications à la planification opérationnelle. Ph.D. thesis, Université Paul Verlaine-Metz (2010) · Zbl 1282.90239
[193] Nguyen, Q.T., Le Thi, H.A.: Solving an inventory routing problem in supply chain by DC programming and DCA. In: Intelligent Information and Database Systems. LNCS, vol. 6592, pp. 432-441. Springer, Berlin Heidelberg (2011) · Zbl 1292.90314
[194] Nguyen, T.A., Nguyen, M.N.: Convergence analysis of a proximal point algorithm for minimizing differences of functions. Optimization 66(1), 129-147 (2017) · Zbl 1364.90266
[195] Nguyen, T.B.T.: La programmation DC et DCA en analyse d’image : acquisition comprimée, segmentation et restauration. Ph.D. thesis, University of Lorraine (2014) · Zbl 1238.68139
[196] Nguyen, TBT; Thi, HA; Le, HM; Vo, XT; Thi, HA (ed.); Nguyen, NT (ed.); Do, T. (ed.), DC approximation approach for \[\ell_0\] ℓ0-minimization in compressed sensing, 37-48 (2015), New York
[197] Nguyen, TMT; Thi, HA; Nguyen, TB (ed.); Do, T. (ed.); Thi, HA (ed.); Nguyen, NT (ed.), A DC programming approach to the continuous equilibrium network design problem, 3-16 (2016), New York
[198] Nguyen, T.P.: Techniques d’optimisation en traitement d’image et vision par ordinateur et en transport logistique. Ph.D. thesis, Université Paul Verlaine-Metz (2007) · Zbl 1393.94020
[199] Nguyen, V.V.: Méthodes exactes pour l’optimisation DC polyédrale en variables mixtes 0-1 basées sur DCA et des nouvelles coupes. Ph.D. thesis, INSA de Rouen (2006) · Zbl 1235.68203
[200] Nguyen Canh, N., Le Thi, H.A., Pham Dinh, T.: A branch and bound algorithm based on DC programming and DCA for strategic capacity planning in supply chain design for a new market opportunity. In: Operations Research Proceedings. Operations Research Proceedings, vol. 2006, pp. 515-520. Springer, Berlin Heidelberg (2007) · Zbl 1209.90047
[201] Nguyen Canh, N.; Pham, TH; Tran, VH; Thi, HA (ed.); Nguyen, NT (ed.); Do, T. (ed.), DC programming and DCA approach for resource allocation optimization in OFDMA/TDD wireless networks, 49-56 (2015), New York · Zbl 1351.90133
[202] Niu, YS; Júdice, J.; Thi, HA; Pham Dinh, T.; Thi, HA (ed.); Pham Dinh, T. (ed.); Nguyen, NT (ed.), Solving the quadratic eigenvalue complementarity problem by DC programming, 203-214 (2015), New York · Zbl 1370.90275
[203] Niu, Y.S., Pham Dinh, T., Le Thi, H.A., Judice, J.: Efficient DC programming approaches for asymmetric eigenvalue complementarity problem. Optim. Methods Softw. 28(4), 812-829 (2013) · Zbl 1307.90145
[204] Ong, C.S., Le Thi, H.A.: Learning sparse classifiers with difference of convex functions algorithms. Optim. Methods Softw. 28(4), 830-854 (2013) · Zbl 1282.90181
[205] Orlov, A., Strekalovsky, A.: On a local search for hexamatrix games. In: A. Kononov, I. Bykadorov, O. Khamisov, I. Davydov, P. Kononova (eds.) DOOR 2016, pp. 477-488 (2016) · Zbl 1229.90121
[206] Ortega, J., Rheinboldt, W.: Iterative Solutions of Nonlinear Equations in Several Variables, pp. 253-255. Academic, New York (1970) · Zbl 0241.65046
[207] Pan, W., Shen, X., Liu, B.: Cluster analysis: unsupervised learning via supervised learning with a non-convex penalty. J. Mach. Learn. Res. 14(1), 1865-1889 (2013) · Zbl 1317.68179
[208] Pang, J.S., Razaviyayn, M., Alvarado, A.: Computing B-stationary points of nonsmooth DC programs. Math. Oper. Res. 42(1), 95-118 (2017) · Zbl 1359.90106
[209] Pang, J.S., Tao, M.: Decomposition methods for computing directional stationary solutions of a class of non-smooth non-convex optimization problems. SIAM J. Optim. (2017, submitted) · Zbl 1142.62027
[210] Parida, P., Das, S.S.: Power allocation in OFDM based NOMA systems: a DC programming approach. In: 2014 IEEE Globecom Workshops (GC Wkshps), pp. 1026-1031. IEEE (2014) · Zbl 1171.62326
[211] Park, F., Lou, Y., Xin, J.: A weighted difference of anisotropic and isotropic total variation for relaxed Mumford-Shah image segmentation. In: IEEE ICIP 2016, pp. 4314-4318 (2016) · Zbl 1142.62027
[212] Park, S.H., Simeone, O., Sahin, O., Shamai, S.: Multihop backhaul compression for the uplink of cloud radio access networks. IEEE Trans. Veh. Technol. 65(5), 3185-3199 (2016)
[213] Pham, V.N.: Programmation DC et DCA pour l’optimisation non convexe/optimisation globale en variables mixtes entières : Codes et Applications. Ph.D. thesis, INSA de Rouen (2013) · Zbl 1102.68605
[214] Pham, V.N., Le Thi, H.A., Pham Dinh, T.: A DC programming framework for portfolio selection by minimizing the transaction costs. In: Advanced Computational Methods for Knowledge Engineering, Studies in Computational Intelligence, vol. 479, pp. 31-40. Springer International Publishing (2013) · Zbl 1237.46007
[215] Pham Dinh, T.: Elements homoduaux d’une matrice \[A\] A relatifs à un couple de normes \[(\phi ,\psi )\](ϕ,ψ). Applications au calcul de \[s_{\phi \psi }(a)\] sϕψ(a) . Séminaire d’Analyse Numérique, Grenoble (1975) · Zbl 1260.49048
[216] Pham Dinh, T.: Calcul du maximum d’une forme quadratique définie positive sur la boule unité de la norme du maximum . Séminaire d’Analyse Numérique, Grenoble (1976) · Zbl 1179.68192
[217] Pham Dinh, T.: Contribution à la théorie de normes et ses applications à l’analyse numérique. Université Joseph Fourier, Grenoble, Thèse de doctorat d’etat es science (1981)
[218] Pham Dinh, T.: Algorithmes de calcul du maximum des formes quadratiques sur la boule unité de la norme du maximum. Numer. Math. 45(3), 377-401 (1984) · Zbl 0531.65022
[219] Pham Dinh, T.: Convergence of a subgradient method for computing the bound norm of matrices. Linear Algebra Appl. 62, 163-182 (1984) · Zbl 0563.65029
[220] Pham Dinh, T., Ho, V.T., Le Thi, H.A.: DC programming and DCA for solving Brugnano-Casulli piecewise linear systems. Comput. Oper. Res. 87(Supplement C), 196-204 (2017) · Zbl 1391.90494
[221] Pham Dinh, T., Le Thi, H.A.: Lagrangian stability and global optimality in nonconvex quadratic minimization over Euclidiean balls and spheres. J. Convex Anal. 2(1-2), 263-276 (1995) · Zbl 0848.49022
[222] Pham Dinh, T., Le Thi, H.A.: Difference of convex function optimization algorithms (DCA) for globally minimizing nonconvex quadratic forms on Euclidean balls and spheres. Oper. Res. Lett. 19(5), 207-216 (1996) · Zbl 0876.90071
[223] Pham Dinh, T., Le Thi, H.A.: Convex analysis approach to D.C. programming: theory, algorithm and applications. Acta Math. Vietnam. 22(1), 289-355 (1997) · Zbl 0895.90152
[224] Pham Dinh, T., Le Thi, H.A.: D.C. optimization algorithms for solving the trust region subproblem. SIAM J. Optim. 8(2), 476-505 (1998) · Zbl 0913.65054
[225] Pham Dinh, T., Le Thi, H.A.: Recent advances in DC programming and DCA. In: Transactions on Computational Intelligence XIII. LNCS, vol. 8342, pp. 1-37. Springer, Berlin Heidelberg (2014)
[226] Pham Dinh, T., Le Thi, H.A., Akoa, F.: Combining DCA and interior point techniques for large-scale nonconvex quadratic programming. Optim. Methods Softw. 23(4), 609-629 (2008) · Zbl 1151.90508
[227] Pham Dinh, T., Le Thi, H.A., Pham, V.N., Niu, Y.S.: DC programming approaches for discrete portfolio optimization under concave transaction costs. Optim. Lett. 10(2), 1-22 (2016) · Zbl 1343.90072
[228] Pham Dinh, T., Nguyen Canh, N., Le Thi, H.A.: DC programming and DCA for globally solving the value-at-risk. Comput. Manag. Sci. 6(4), 477-501 (2009) · Zbl 1177.90286
[229] Pham Dinh, T., Nguyen Canh, N., Le Thi, H.A.: An efficient combination of DCA and B&B using DC/SDP relaxation for globally solving binary quadratic programs. J. Global Optim. 48(4), 595-632 (2010) · Zbl 1226.90060
[230] Pham Dinh, T., Niu, Y.S.: An efficient DC programming approach for portfolio decision with higher moments. Comput. Optim. Appl. 50(3), 525-554 (2011) · Zbl 1237.90186
[231] Pham Dinh, T., Pham, V.N., Le Thi, H.A.: DC programming and DCA for portfolio optimization with linear and fixed transaction costs. In: Intelligent Information and Database Systems, LNCS, vol. 8398, pp. 392-402. Springer International Publishing (2014) · Zbl 1156.68054
[232] Pham Dinh, T.; Souad, EB; Hiriart-Urruty, JB (ed.), Algorithms for solving a class of nonconvex optimization problems. Methods of subgradients, No. 129, 249-271 (1986), Amsterdam
[233] Pham Dinh, T., Souad, E.B.: Duality in D.C. (difference of convex functions) optimization. Subgradient methods. In: Trends in Mathematical Optimization, International Series of Numerical Mathematics, vol. 84, pp. 276-294. Birkhäuser, Basel (1988)
[234] Phan, A.H., Tuan, H.D., Kha, H.H.: D.C. iterations for SINR maximin multicasting in cognitive radio. In: 6th International Conference on Signal Processing and Communication Systems (ICSPCS 2012), pp. 1-5 (2012) · Zbl 1045.90074
[235] Phan, D.N.: DCA based algorithms for learning with sparsity in high dimensional setting and stochastical learning. Ph.D. thesis, University of Lorraine (2016)
[236] Phan, D.N., Le Thi, H.A., Pham Dinh, T.: Sparse covariance matrix estimation by DCA-based algorithms. Neural Comput. 29(11), 3040-3077 (2017) · Zbl 1418.62276
[237] Piot, B.; Geist, M.; Pietquin, O.; Ghahramani, Z. (ed.); Welling, M. (ed.); Cortes, C. (ed.); Lawrence, ND (ed.); Weinberger, KQ (ed.), Difference of convex functions programming for reinforcement learning, No. 27, 2519-2527 (2014), Red Hook
[238] Polyak, B.T.: Introduction to Optimization. Optimization Software. Inc. Publication Division, New York (1987) · Zbl 0708.90083
[239] Poulakis, M.I., Vassaki, S., Panagopoulos, A.D.: Secure cooperative communications under secrecy outage constraint: a DC programming approach. IEEE Wirel. Commun. Lett. 5(3), 332-335 (2016)
[240] Queiroz, M., Júdice, J., Humes, C.: The symmetric eigenvalue complementarity problem. Math. Comput. 73(248), 1849-1863 (2004) · Zbl 1119.90059
[241] Rakotomamonjy, A., Flamary, R., Gasso, G.: DC proximal newton for nonconvex optimization problems. IEEE Trans. Neural Netw. Learn. Syst. 27(3), 636-647 (2016)
[242] Razaviyayn, M.: Successive convex approximation: analysis and applications. Ph.D. thesis, University of Minnesota (2014) · Zbl 1213.90176
[243] Razaviyayn, M., Hong, M., Luo, Z.Q.: A unified convergence analysis of block successive minimization methods for nonsmooth optimization. SIAM J. Optim. 23(2), 1126-1153 (2013) · Zbl 1273.90123
[244] Razaviyayn, M.; Hong, M.; Luo, ZQ; Pang, JS; Ghahramani, Z. (ed.); Welling, M. (ed.); Cortes, C. (ed.); Lawrence, N. (ed.); Weinberger, K. (ed.), Parallel successive convex approximation for nonsmooth nonconvex optimization, No. 27, 1440-1448 (2014), Red Hook
[245] Razaviyayn, M., Sanjabi, M., Luo, Z.Q.: A stochastic successive minimization method for nonsmooth nonconvex optimization with applications to transceiver design in wireless communication networks. Math. Program. 157(2), 515-545 (2016) · Zbl 1357.90101
[246] Robbins, H., Monro, S.: A stochastic approximation method. Ann. Math. Stat. 22(3), 400-407 (1951) · Zbl 0054.05901
[247] Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970) · Zbl 0193.18401
[248] Rockafellar, R.T.: Monotone operators and the proximal point algorithm. SIAM J. Control Optim. 14(5), 877-898 (1976) · Zbl 0358.90053
[249] Schad, A., Law, K.L., Pesavento, M.: Rank-two beamforming and power allocation in multicasting relay networks. IEEE Trans Signal Process. 63(13), 3435-3447 (2015) · Zbl 1394.94503
[250] Schleich, J., Le Thi, H.A., Bouvry, P.: Solving the minimum \[m\] m-dominating set problem by a continuous optimization approach based on DC programming and DCA. J. Comb. Optim. 24(4), 397-412 (2012) · Zbl 1261.90082
[251] Schnörr, C.: Signal and image approximation with level-set constraints. Computing 81(2), 137-160 (2007) · Zbl 1156.68054
[252] Schüle, T., Schnörr, C., Weber, S., Hornegger, J.: Discrete tomography by convex-concave regularization and D.C. programming. Discrete Appl. Math. 151(1-3), 229-243 (2005) · Zbl 1131.68571
[253] Schüle, T., Weber, S., Schnörr, C.: Adaptive reconstruction of discrete-valued objects from few projections. Electron. Notes Discrete Math. 20, 365-384 (2005) · Zbl 1179.68190
[254] Scutari, G., Facchinei, F., Lampariello, L.: Parallel and distributed methods for constrained nonconvex optimization-part I: theory. IEEE Trans. Signal Process. 65(8), 1929-1944 (2017) · Zbl 1414.90290
[255] Scutari, G., Facchinei, F., Lampariello, L., Sardellitti, S., Song, P.: Parallel and distributed methods for constrained nonconvex optimization-part II: applications in communications and machine learning. IEEE Trans. Signal Process. 65(8), 1945-1960 (2017) · Zbl 1414.90291
[256] Scutari, G., Facchinei, F., Song, P., Palomar, D.P., Pang, J.S.: Decomposition by partial linearization: parallel optimization of multi-agent systems. IEEE Trans. Signal Process. 62(3), 641-656 (2014) · Zbl 1394.94507
[257] Seeger, A.: Quadratic eigenvalue problems under conic constraints. SIAM J. Matrix Anal. A 32(3), 700-721 (2011) · Zbl 1234.15003
[258] Shen, X., Huang, H.C.: Simultaneous supervised clustering and feature selection over a graph. Biometrika 99(4), 899-914 (2012) · Zbl 1452.62467
[259] Shen, X., Tseng, G.C., Zhang, X., Wong, W.H.: On \[\psi\] ψ learning. J. Am. Stat. Assoc. 98, 724-734 (2003) · Zbl 1052.62095
[260] Slawski, M.; Hein, M.; Lutsik, P.; Burges, CJC (ed.); Bottou, L. (ed.); Welling, M. (ed.); Ghahramani, Z. (ed.); Weinberger, KQ (ed.), Matrix factorization with binary components, No. 26, 3210-3218 (2013), Red Hook
[261] Smola, A.J., Song, L., Teo, C.H.: Relative novelty detection. In: Proceedings of the 12th International Conference on Artificial Intelligence and Statistics, vol. 5. JMLR W&CP 5, pp. 536-543 (2009)
[262] Song, Y., Lin, L., Jian, L.: Robust check loss-based variable selection of high-dimensional single-index varying-coefficient model. Commun. Nonlinear Sci. 36, 109-128 (2016) · Zbl 1470.62116
[263] Sriperumbudur, B.K., Torres, D.A., Lanckriet, G.R.G.: Sparse eigen methods by D.C. programming. In: ICML’07, pp. 831-838. ACM, New York, NY, USA (2007) · Zbl 1300.90029
[264] Sun, Q., Xiang, S., Ye, J.: Robust principal component analysis via capped norms. In: Proceedings of the 19th ACM SIGKDD, KDD’13, pp. 311-319. ACM (2013)
[265] Sun, W., Sampaio, J.B., Candido, R.M.: Proximal point algorithm for minimization of DC function. J. Comput. Math. 21, 451-462 (2003) · Zbl 1107.90427
[266] Ta, A.S.: Programmation DC et DCA pour la résolution de certaines classes des problèmes dans les systèmes de transport et de communication. Ph.D. thesis, INSA - Rouen (2012)
[267] Ta, A.S., Le Thi, H.A., Arnould, G., Khadraoui, D., Pham Dinh, T.: Solving car pooling problem using DCA. In: Global Information Infrastructure Symposium (GIIS 2011), pp. 1-6 (2011)
[268] Ta, AS; Thi, HA; Ha, TS; Thi, HA (ed.); Pham Dinh, T. (ed.); Nguyen, NT (ed.), Solving relaxation orienteering problem using DCA-CUT, 191-202 (2015), New York · Zbl 1370.90228
[269] Ta, A.S., Le Thi, H.A., Khadraoui, D., Pham Dinh, T.: Solving multicast QoS routing problem in the context V2I communication services using DCA. In: IEEE/ACIS 9th International Conference on Computer and Information Science (ICIS), 2010, pp. 471-476 (2010) · Zbl 1339.92064
[270] Ta, A.S., Le Thi, H.A., Khadraoui, D., Pham Dinh, T.: Solving QoS routing problems by DCA. In: Intelligent Information and Database Systems. LNCS, vol. 5991, pp. 460-470. Springer, Berlin Heidelberg (2010) · Zbl 1045.90074
[271] Ta, A.S., Le Thi, H.A., Khadraoui, D., Pham Dinh, T.: Solving partitioning-hub location-routing problem using DCA. J. Ind. Manag. Optim. 8(1), 87-102 (2012) · Zbl 1364.90219
[272] Ta, A.S., Pham Dinh, T., Le Thi, H.A., Khadraoui, D.: Solving many to many multicast QoS routing problem using DCA and proximal decomposition technique. In: International Conference on Computing, Networking and Communications (ICNC 2012), pp. 809-814 (2012)
[273] Ta, M.T.: Techniques d’optimisation non convexe basée sur la programmation DC et DCA et méthodes évolutives pour la classification non supervisée. Ph.D. thesis, University of Lorraine (2014)
[274] Ta, MT; Thi, HA; Boudjeloud-Assala, L.; Perner, P. (ed.), Clustering data stream by a sub-window approach using DCA, 279-292 (2012), Berlin
[275] Ta, MT; Thi, HA; Boudjeloud-Assala, L.; Nguyen, TN (ed.); Do, T. (ed.); Thi, AH (ed.), Clustering data streams over sliding windows by DCA, 65-75 (2013), Heidelberg
[276] Ta, M.T., Le Thi, H.A., Boudjeloud-Assala, L.: An efficient clustering method for massive dataset based on DC programming and DCA approach. In: Lee, M., Hirose, A., Hou, Z.G., Kil, R.M. (eds.) ICONIP 2013, Part II, LNCS, vol. 8227, pp. 538-545. Springer, Berlin Heidelberg (2013)
[277] Taleb, D., Liu, Y., Pesavento, M.: Full-rate general rank beamforming in single-group multicasting networks using non-orthogonal STBC. In: 24th EUSIPCO, pp. 2365-2369 (2016) · Zbl 0912.90233
[278] Thai, J., Hunter, T., Akametalu, A.K., Tomlin, C.J., Bayen, A.M.: Inverse covariance estimation from data with missing values using the concave-convex procedure. In: 53rd IEEE Conference on Decision and Control, pp. 5736-5742 (2014) · Zbl 0905.90131
[279] Thanh, P.N., Bostel, N., Péton, O.: A DC programming heuristic applied to the logistics network design problem. Int. J. Prod. Econ. 135(1), 94-105 (2012)
[280] Thiao, M.: Pham Dinh, T., Le Thi, H.A.: DC programming approach for a class of nonconvex programs involving \[\ell_0\] ℓ0 norm. Modelling. In: Computation and Optimization in Information Systems and Management Sciences, Communications in Computer and Information Science, vol. 14, pp. 348-357. Springer, Berlin Heidelberg (2008) · Zbl 1160.90626
[281] Thiao, M., Pham Dinh, T., Le Thi, H.A.: A DC programming approach for sparse eigenvalue problem. In: Fürnkranz, J., Joachims, T. (eds.) Proceedings ICML-10, pp. 1063-1070. Omnipress (2010)
[282] Tian, X., Gasso, G., Canu, S.: A multiple kernel framework for inductive semi-supervised SVM learning. Neurocomputing 90, 46-58 (2012)
[283] Torres, D.A., Turnbull, D., Sriperumbudur, B.K., Barrington, L., Lanckriet, G.R.G.: Finding musically meaningful words by sparse CCA. In: NIPS Workshop on Music, the Brain and Cognition (2007) · Zbl 1370.90228
[284] Tran, D.Q., Le Thi, H.A., Adjallah, K.H.: DCA for minimizing the cost and tardiness of preventive maintenance tasks under real-time allocation constraint. In: Nguyen, N.T., Le, M.T., Swiatek, J. (eds.) Intelligent Information and Database Systems, LNCS, vol. 5991, pp. 410-419. Springer, Berlin Heidelberg (2010) · Zbl 1192.90081
[285] Tran, D.Q., Nguyen, B.T.P., Nguyen, Q.T.: A new approach for optimizing traffic signals in networks considering rerouting. In: Modelling, Computation and Optimization in Information Systems and Management Sciences, Advances in Intelligent Systems and Computing, vol. 359, pp. 143-154. Springer International Publishing (2015) · Zbl 1370.90080
[286] Tran, T.T., Le Thi, H.A., Pham Dinh, T.: DC programming and DCA for a novel resource allocation problem in emerging area of cooperative physical layer security. In: Advanced Computational Methods for Knowledge Engineering, Advances in Intelligent Systems and Computing 358, 57-68 (2015) · Zbl 1350.90030
[287] Tran, T.T., Le Thi, H.A., Pham Dinh, T.: DC programming and DCA for enhancing physical layer security via cooperative jamming. Comput. Oper. Res. 87(Supplement C), 235-244 (2017) · Zbl 1391.90166
[288] Tran, T.T., Tuan, N.N., Le Thi, H.A., Gély, A.: DC programming and DCA for enhancing physical layer security via relay beamforming strategies. In: Nguyen, N.T., Trawiński, B., Fujita, H., Hong, T.P. (eds.) ACIIDS 2016, Part II, LNAI 9622, pp. 640-650. Springer, Berlin Heidelberg (2016) · Zbl 1022.68112
[289] Tsiligkaridis, T., Marcheret, E., Goel, V.: A difference of convex functions approach to large-scale log-linear model estimation. IEEE Trans. Audio Speech 21(11), 2255-2266 (2013)
[290] Tuan, H.N.: Convergence rate of the Pham Dinh-Le Thi algorithm for the trust-region subproblem. J. Optim. Theory Appl. 154(3), 904-915 (2012) · Zbl 1256.90032
[291] Tuan, H.N., Yen, N.D.: Convergence of Pham Dinh-Le Thi’s algorithm for the trust-region subproblem. J. Global Optim. 55(2), 337-347 (2013) · Zbl 1287.90046
[292] Vanderbei, R.J.: LOQO: an interior point code for quadratic programming. Optim. Methods Softw. 11(1-4), 451-484 (1999) · Zbl 0973.90518
[293] Vasiloglou, N., Gray, A.G., Anderson, D.V.: Non-negative matrix factorization, convexity and isometry. In: Proceedings of the 2009 SIAM ICDM, chap. 57, pp. 673-684 (2009)
[294] Vavasis, S.A.: Nonlinear Optimization: Complexity Issues. Oxford University Press, Oxford (1991) · Zbl 0785.90091
[295] Vo, X.T.: Learning with sparsity and uncertainty by difference of convex functions optimization. Ph.D. thesis, University of Lorraine (2015) · Zbl 1075.90071
[296] Vo, X.T., Le Thi, H.A.: Pham Dinh, T.: Robust optimization for clustering. ACIIDS 2016. Part II, LNCS, vol. 9622, pp. 1-10. Springer, Berlin Heidelberg (2016) · Zbl 1160.91015
[297] Vo, X.T., Le Thi, H.A., Pham Dinh, T., Nguyen, T.B.T.: DC programming and DCA for dictionary learning. In: Computational Collective Intelligence, LNCS, vol. 9329, pp. 295-304. Springer International Publishing (2015)
[298] Vo, X.T., Tran, B., Le Thi, H.A., Pham Dinh, T.: Ramp loss support vector data description. In: Proc. 9th Asian Conference on Intelligent Information and Database Systems (ACIIDS 2017). 3-5 April 2017, Kanazawa, Japan (2017). Lecture Note in Computer Science. Springer (2017, to appear) · Zbl 1248.65067
[299] Vucic, N., Shi, S., Schubert, M.: DC programming approach for resource allocation in wireless networks. In: Proceedings of the 8th International Symposium on Modeling and Optimization in Mobile, Ad Hoc and Wireless Networks (WiOpt 2010), pp. 380-386 (2010)
[300] Wang, D., Chen, W., Han, Z.: Energy efficient secure communication over decode-and-forward relay channels. IEEE Trans. Commun. 63(3), 892-905 (2015)
[301] Wang, F., Zhao, B., Zhang, C.: Linear time maximum margin clustering. IEEE Trans. Neural Netw. 21(2), 319-332 (2010)
[302] Wang, J., Shen, X.: Large margin semi-supervised learning. J. Mach. Learn. Res. 8, 1867-1891 (2007) · Zbl 1222.68329
[303] Wang, J., Shen, X., Pan, W.: On transductive support vector machines. In: Prediction and Discovery, Contemporary Mathematics 443, pp. 7-19. American Mathematical Society (2007) · Zbl 1147.68657
[304] Wang, J., Shen, X., Pan, W.: On efficient large margin semisupervised learning: method and theory. J. Mach. Learn. Res. 10, 719-742 (2009) · Zbl 1235.68203
[305] Wang, K., Zhong, P., Zhao, Y.: Training robust support vector regression via D.C. program. J. Inf. Comput. Sci. 7(12), 2385-2394 (2010)
[306] Wang, K., Zhu, W., Zhong, P.: Robust support vector regression with generalized loss function and applications. Neural Process. Lett. 41(1), 89-106 (2015)
[307] Wang, L., Kim, Y., Li, R.: Calibrating nonconvex penalized regression in ultra-high dimension. Ann. Stat. 41(5), 2505-2536 (2013) · Zbl 1281.62106
[308] Wang, Y., Xia, X.: An effective \[l_0\] l0-svm classifier for face recognition based on haar features. Adv. Nat. Sci. 9(1), 1-4 (2016)
[309] Weber, S., Schüle, T., Schnörr, C.: Prior learning and convex-concave regularization of binary tomography. Electron. Notes Discrete Math. 20, 313-327 (2005) · Zbl 1179.68192
[310] Weston, J., Elisseeff, A., Schölkopf, B., Tipping, M.: Use of the zero-norm with linear models and kernel methods. J. Mach. Learn. Res. 3, 1439-1461 (2003) · Zbl 1102.68605
[311] Wozabal, D.: Value-at-risk optimization using the difference of convex algorithm. OR Spectrum 34(4), 861-883 (2012) · Zbl 1282.91313
[312] Wu, C., Kwon, S., Shen, X., Pan, W.: A new algorithm and theory for penalized regression-based clustering. J. Mach. Learn. Res. 17, 1-25 (2016) · Zbl 1392.68371
[313] Wu, C., Li, C., Long, Q.: A DC Programming approach for sensor network localization with uncertainties in anchor positions. J. Ind. Manag. Optim. 10(3), 817-826 (2014) · Zbl 1292.90314
[314] Wu, Y., Liu, Y.: Robust truncated hinge loss support vector machines. J. Am. Stat. Assoc. 102(479), 974-983 (2007) · Zbl 1469.62293
[315] Wu, Y., Liu, Y.: Variable selection in quantile regression. Stat Sin. 19, 801-817 (2009) · Zbl 1166.62012
[316] Xiang, S., Shen, X., Ye, J.: Efficient nonconvex sparse group feature selection via continuous and discrete optimization. Artif. Intell. 224, 28-50 (2015) · Zbl 1343.68210
[317] Yang, L., Ju, R.: A DC programming approach for feature selection in the minimax probability machine. Int. J. Comput. Intell. Syst. 7(1), 12-24 (2014)
[318] Yang, L., Qian, Y.: A sparse logistic regression framework by difference of convex functions programming. Appl. Intell. 45(2), 241-254 (2016)
[319] Yang, L., Wang, L.: A class of semi-supervised support vector machines by DC programming. Adv. Data Anal. Classif. 7(4), 417-433 (2013) · Zbl 1308.90138
[320] Yang, L., Zhang, S.: A sparse extreme learning machine framework by continuous optimization algorithms and its application in pattern recognition. Eng. Appl. Artif. Int. 53, 176-189 (2016)
[321] Yang, S., Yuan, L., Lai, Y.C., Shen, X., Wonka, P., Ye, J.: Feature grouping and selection over an undirected graph. In: ACM SIGKDD, pp. 922-930 (2012)
[322] Yang, T., Liu, J., Gong, P., Zhang, R., Shen, X., Ye, J.: Absolute fused lasso and its application to genome-wide association studies. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, KDD’16, pp. 1955-1964. ACM (2016) · Zbl 1131.68571
[323] Yin, P., Lou, Y., He, Q., Xin, J.: Minimization of \[\ell_{1-2}\] ℓ1-2 for compressed sensing. SIAM J. Sci. Comput. 37(1), 536-563 (2015)
[324] Yin, P., Xin, J., Qi, Y.: Linear feature transform and enhancement of classification on deep neural network. (2016, Submitted) · Zbl 1484.68210
[325] Ying, Y., Huang, K., Campbell, C.: Enhanced protein fold recognition through a novel data integration approach. BMC Bioinform. 10(1), 1-18 (2009)
[326] You, S., Lijun, C., Liu, Y.E.: Convex-concave procedure for weighted sum-rate maximization in a MIMO interference network. In: IEEE GLOBECOM 2014, pp. 4060-4065 (2014) · Zbl 1322.90072
[327] Yu, C.N.J., Joachims, T.: Learning structural SVMs with latent variables. In: ICML’09, pp. 1169-1176. ACM, New York, NY, USA (2009)
[328] Yu, P.L.: Multiple-Criteria Decision Making: Concepts, Techniques, and Extensions. In: Mathematical Concepts and Methods in Science and Engineering, vol. 30. Springer, USA (1985)
[329] Yuille, A.L., Rangarajan, A.: The concave-convex procedure. Neural Comput. 15(4), 915-936 (2003) · Zbl 1022.68112
[330] Zhang, K., Tsang, I.W., Kwok, J.T.: Maximum margin clustering made practical. IEEE Trans. Neural Netw. 20(4), 583-596 (2009)
[331] Zhang, P., Tian, Y., Zhang, Z., Li, A., Zhu, X.: Select objective functions for multiple criteria programming classification. In: Web Intelligence and Intelligent Agent Technology, 2008. WI-IAT’08. IEEE/WIC/ACM International Conference on, vol. 3, pp. 420-423 (2008) · Zbl 1198.90327
[332] Zhang, X., Wu, Y., Wang, L., Li, R.: Variable selection for support vector machines in moderately high dimensions. J. R. Stat. Soc. B 78(1), 53-76 (2016) · Zbl 1411.62176
[333] Zhao, Z., Sun, L., Yu, S., Liu, H., Ye, J.: Multiclass probabilistic kernel discriminant analysis. In: Proceedings of the 21st International Joint Conference on Artifical Intelligence, IJCAI’09, pp. 1363-1368. Morgan Kaufmann (2009) · Zbl 1307.90145
[334] Zheng, G.: Joint beamforming optimization and power control for full-duplex MIMO two-way relay channel. IEEE Trans. Signal Process. 63(3), 555-566 (2015) · Zbl 1394.94916
[335] Zheng, G., Krikidis, I., Li, J., Petropulu, A.P., Ottersten, B.: Improving physical layer secrecy using full-duplex jamming receivers. IEEE Trans. Signal Process. 61(20), 4962-4974 (2013) · Zbl 1393.94918
[336] Zhong, P.: Training robust support vector regression with smooth non-convex loss function. Optim. Methods Softw. 27(6), 1039-1058 (2012) · Zbl 1248.65067
[337] Zhong, Y., Aghezzaf, E.H.: Combining DC-programming and steepest-descent to solve the single-vehicle inventory routing problem. Comput. Ind. Eng. 61(2), 313-321 (2011)
[338] Zhou, Y., Zhu, Y., Xue, Z.: Enhanced MIMOME wiretap channel via adopting full-duplex MIMO radios. In: 2014 IEEE Global Communications Conference, pp. 3320-3325. IEEE (2014) · Zbl 1359.90106
[339] Zhou, Z.H., Zhang, M.L., Huang, S.J., Li, Y.F.: Multi-instance multi-label learning. Artif. Intell. 176(1), 2291-2320 (2012) · Zbl 1238.68139
[340] Zhu, Y., Shen, X., Pan, W.: Simultaneous grouping pursuit and feature selection over an undirected graph. J. Am. Stat. Assoc. 108(502), 713-725 (2013) · Zbl 06195973
[341] Zisler, M., Petra, S., Schnörr, C., Schnörr, C.: Discrete tomography by continuous multilabeling subject to projection constraints. In: Proceedings of the 38th German Conference on Pattern Recognition (2016)
[342] Zou, H.: The adaptive lasso and its oracle properties. J. Am. Stat. Assoc. 2006(476), 1418-1429 (2006) · Zbl 1171.62326
[343] Zou, H., Li, R.: One-step sparse estimates in nonconcave penalized likelihood models. Ann. Stat. 36(4), 1509-1533 (2008) · Zbl 1142.62027
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.