Wang, Shiwei; Ding, Chao; Zhang, Yangjing; Zhao, Xinyuan Strong variational sufficiency for nonlinear semidefinite programming and its implications. (English) Zbl 1527.49013 SIAM J. Optim. 33, No. 4, 2988-3011 (2023). MSC: 49J52 90C22 90C46 PDFBibTeX XMLCite \textit{S. Wang} et al., SIAM J. Optim. 33, No. 4, 2988--3011 (2023; Zbl 1527.49013) Full Text: DOI arXiv
Xu, Yingrang; Li, Shengjie Optimality conditions for multiobjective optimization problems via image space analysis. (English) Zbl 1522.90190 Numer. Funct. Anal. Optim. 44, No. 7, 708-723 (2023). MSC: 90C29 90C46 PDFBibTeX XMLCite \textit{Y. Xu} and \textit{S. Li}, Numer. Funct. Anal. Optim. 44, No. 7, 708--723 (2023; Zbl 1522.90190) Full Text: DOI
Chen, Jiawei; Deng, Guangju; Zhang, Tao A unified duality of multiobjective optimization problem with uncertainty data. (English) Zbl 1462.90149 J. Nonlinear Convex Anal. 21, No. 10, 2273-2286 (2020). MSC: 90C46 90C29 PDFBibTeX XMLCite \textit{J. Chen} et al., J. Nonlinear Convex Anal. 21, No. 10, 2273--2286 (2020; Zbl 1462.90149) Full Text: Link
Gu, Xiaoyi; Ahmed, Shabbir; Dey, Santanu S. Exact augmented Lagrangian duality for mixed integer quadratic programming. (English) Zbl 1515.90078 SIAM J. Optim. 30, No. 1, 781-797 (2020). MSC: 90C11 90C20 90C46 PDFBibTeX XMLCite \textit{X. Gu} et al., SIAM J. Optim. 30, No. 1, 781--797 (2020; Zbl 1515.90078) Full Text: DOI arXiv
Son, T. Q.; Wen, C. F. Weak-subdifferentials for vector functions and applications to multiobjective semi-infinite optimization problems. (English) Zbl 1451.90133 Appl. Anal. 99, No. 5, 840-855 (2020). Reviewer: Jan-Joachim Rückmann (Bergen) MSC: 90C26 90C34 49N15 90C46 PDFBibTeX XMLCite \textit{T. Q. Son} and \textit{C. F. Wen}, Appl. Anal. 99, No. 5, 840--855 (2020; Zbl 1451.90133) Full Text: DOI
Zhao, Chen; Luo, Ziyan; Li, Weiyue; Qi, Houduo; Xiu, Naihua Lagrangian duality and saddle points for sparse linear programming. (English) Zbl 1432.90127 Sci. China, Math. 62, No. 10, 2015-2032 (2019). MSC: 90C26 90C30 90C46 PDFBibTeX XMLCite \textit{C. Zhao} et al., Sci. China, Math. 62, No. 10, 2015--2032 (2019; Zbl 1432.90127) Full Text: DOI Link
Adıvar, Murat; Fang, Shu-Cherng Convex analysis and duality over discrete domains. (English) Zbl 1413.90184 J. Oper. Res. Soc. China 6, No. 2, 189-247 (2018). MSC: 90C10 90C46 90C05 PDFBibTeX XMLCite \textit{M. Adıvar} and \textit{S.-C. Fang}, J. Oper. Res. Soc. China 6, No. 2, 189--247 (2018; Zbl 1413.90184) Full Text: DOI
Zhao, Xiaopeng Constraint qualification for quasiconvex inequality system with applications in constraint optimization. (English) Zbl 1466.90114 J. Nonlinear Convex Anal. 17, No. 5, 879-889 (2016). MSC: 90C34 90C26 90C46 PDFBibTeX XMLCite \textit{X. Zhao}, J. Nonlinear Convex Anal. 17, No. 5, 879--889 (2016; Zbl 1466.90114) Full Text: Link
Luo, Honglin; Peng, Jianwen; Yao, Jen-Chih Generalized weak sharp minima and the existence of strong Lagrangian multipliers in conic convex optimization. (English) Zbl 1353.90111 J. Nonlinear Convex Anal. 17, No. 9, 1791-1811 (2016). MSC: 90C25 90C30 90C31 49N15 PDFBibTeX XMLCite \textit{H. Luo} et al., J. Nonlinear Convex Anal. 17, No. 9, 1791--1811 (2016; Zbl 1353.90111) Full Text: Link
Li, Chong; Zhao, Xiaopeng; Hu, Yaohua Quasi-Slater and Farkas-Minkowski qualifications for semi-infinite programming with applications. (English) Zbl 1298.90119 SIAM J. Optim. 23, No. 4, 2208-2230 (2013). Reviewer: Gerhard-Wilhelm Weber (Ankara) MSC: 90C34 90C25 41A29 90C46 PDFBibTeX XMLCite \textit{C. Li} et al., SIAM J. Optim. 23, No. 4, 2208--2230 (2013; Zbl 1298.90119) Full Text: DOI
Bhatia, Guneet; Sahay, Rishi Rajan Strict global minimizers and higher-order generalized strong invexity in multiobjective optimization. (English) Zbl 1282.90163 J. Inequal. Appl. 2013, Paper No. 31, 14 p. (2013). MSC: 90C29 90C46 26A51 PDFBibTeX XMLCite \textit{G. Bhatia} and \textit{R. R. Sahay}, J. Inequal. Appl. 2013, Paper No. 31, 14 p. (2013; Zbl 1282.90163) Full Text: DOI
Flores-Bazán, Fabián; Mastroeni, Giandomenico Strong duality in cone constrained nonconvex optimization. (English) Zbl 1285.90077 SIAM J. Optim. 23, No. 1, 153-169 (2013). Reviewer: Stephan Dempe (Freiberg) MSC: 90C46 90C30 49N15 PDFBibTeX XMLCite \textit{F. Flores-Bazán} and \textit{G. Mastroeni}, SIAM J. Optim. 23, No. 1, 153--169 (2013; Zbl 1285.90077) Full Text: DOI
Guerra-Vázquez, Francisco; Rückmann, Jan-J.; Werner, Ralf On saddle points in nonconvex semi-infinite programming. (English) Zbl 1303.90109 J. Glob. Optim. 54, No. 3, 433-447 (2012). Reviewer: Armin Hoffmann (Ilmenau) MSC: 90C34 90C26 90C46 PDFBibTeX XMLCite \textit{F. Guerra-Vázquez} et al., J. Glob. Optim. 54, No. 3, 433--447 (2012; Zbl 1303.90109) Full Text: DOI
Son, T. Q.; Kim, D. S.; Tam, N. N. Weak stability and strong duality of a class of nonconvex infinite programs via augmented Lagrangian. (English) Zbl 1278.90391 J. Glob. Optim. 53, No. 2, 165-184 (2012). MSC: 90C30 90C46 90C31 PDFBibTeX XMLCite \textit{T. Q. Son} et al., J. Glob. Optim. 53, No. 2, 165--184 (2012; Zbl 1278.90391) Full Text: DOI
Komargodski, Zohar Vector mesons and an interpretation of Seiberg duality. (English) Zbl 1294.81288 J. High Energy Phys. 2011, No. 2, Paper No. 019, 21 p. (2011). MSC: 81V05 81T60 81V35 70S05 PDFBibTeX XMLCite \textit{Z. Komargodski}, J. High Energy Phys. 2011, No. 2, Paper No. 019, 21 p. (2011; Zbl 1294.81288) Full Text: DOI arXiv
Chen, Chunrong; Cheng, T. C. Edwin; Li, Shengjie; Yang, Xiaoqi Nonlinear augmented Lagrangian for nonconvex multiobjective optimization. (English) Zbl 1214.90108 J. Ind. Manag. Optim. 7, No. 1, 157-174 (2011). MSC: 90C29 90C46 PDFBibTeX XMLCite \textit{C. Chen} et al., J. Ind. Manag. Optim. 7, No. 1, 157--174 (2011; Zbl 1214.90108) Full Text: DOI
Jeyakumar, V.; Li, Guoyin Regularized Lagrangian duality for linearly constrained quadratic optimization and trust-region problems. (English) Zbl 1230.90145 J. Glob. Optim. 49, No. 1, 1-14 (2011). MSC: 90C20 90C46 90C26 90C30 PDFBibTeX XMLCite \textit{V. Jeyakumar} and \textit{G. Li}, J. Glob. Optim. 49, No. 1, 1--14 (2011; Zbl 1230.90145) Full Text: DOI
Jeyakumar, V.; Li, G. Y. Strong duality in robust convex programming: complete characterizations. (English) Zbl 1228.90075 SIAM J. Optim. 20, No. 6, 3384-3407 (2010). Reviewer: Rembert Reemtsen (Cottbus) MSC: 90C25 90C46 90C30 PDFBibTeX XMLCite \textit{V. Jeyakumar} and \textit{G. Y. Li}, SIAM J. Optim. 20, No. 6, 3384--3407 (2010; Zbl 1228.90075) Full Text: DOI
Fang, D. H.; Li, C.; Ng, K. F. Constraint qualifications for extended Farkas’s lemmas and Lagrangian dualities in convex infinite programming. (English) Zbl 1206.90198 SIAM J. Optim. 20, No. 3, 1311-1332 (2009). Reviewer: Francisco Guerra Vazquez (Puebla) MSC: 90C34 90C25 52A07 41A29 90C46 PDFBibTeX XMLCite \textit{D. H. Fang} et al., SIAM J. Optim. 20, No. 3, 1311--1332 (2009; Zbl 1206.90198) Full Text: DOI
Ai, Wenbao; Zhang, Shuzhong Strong duality for the CDT subproblem: a necessary and sufficient condition. (English) Zbl 1187.90290 SIAM J. Optim. 19, No. 4, 1735-1756 (2009). Reviewer: Qamrul Hasan Ansari (Aligarh) MSC: 90C33 90C51 90C05 PDFBibTeX XMLCite \textit{W. Ai} and \textit{S. Zhang}, SIAM J. Optim. 19, No. 4, 1735--1756 (2009; Zbl 1187.90290) Full Text: DOI
Chen, Zhe Generalized augmented Lagrangian duality theory and applications in vector optimization problems. (Chinese. English summary) Zbl 1174.49321 Acta Math. Sci., Ser. A, Chin. Ed. 28, No. 3, 570-577 (2008). MSC: 49N15 90C46 PDFBibTeX XMLCite \textit{Z. Chen}, Acta Math. Sci., Ser. A, Chin. Ed. 28, No. 3, 570--577 (2008; Zbl 1174.49321)
Bhatia, Guneet Optimality and mixed saddle point criteria in multiobjective optimization. (English) Zbl 1144.90023 J. Math. Anal. Appl. 342, No. 1, 135-145 (2008). Reviewer: Francisco Guerra Vazquez (Puebla) MSC: 90C29 90C46 PDFBibTeX XMLCite \textit{G. Bhatia}, J. Math. Anal. Appl. 342, No. 1, 135--145 (2008; Zbl 1144.90023) Full Text: DOI
Li, D.; Sun, X. L. Towards strong duality in integer programming. (English) Zbl 1097.90068 J. Glob. Optim. 35, No. 2, 255-282 (2006). MSC: 90C46 90C10 PDFBibTeX XMLCite \textit{D. Li} and \textit{X. L. Sun}, J. Glob. Optim. 35, No. 2, 255--282 (2006; Zbl 1097.90068) Full Text: DOI
Wolkowicz, Henry A note on lack of strong duality for quadratic problems with orthogonal constraints. (English) Zbl 1058.90046 Eur. J. Oper. Res. 143, No. 2, 356-364 (2002). MSC: 90C20 90C46 PDFBibTeX XMLCite \textit{H. Wolkowicz}, Eur. J. Oper. Res. 143, No. 2, 356--364 (2002; Zbl 1058.90046) Full Text: DOI
O’Raifeartaigh, L. Noether currents for \(N=2\) SUSY QCD. (English) Zbl 1043.81747 Doebner, H.-D. (ed.) et al., Quantum theory and symmetries. Proceedings of the international symposium held in Goslar, Germany, July 18–22, 1999. Singapore: World Scientific (ISBN 981-02-4237-9). 323-330 (2000). MSC: 81V05 81T60 PDFBibTeX XMLCite \textit{L. O'Raifeartaigh}, in: Quantum theory and symmetries. Proceedings of the international symposium held in Goslar, Germany, July 18--22, 1999. Singapore: World Scientific. 323--330 (2000; Zbl 1043.81747)
Anstreicher, Kurt; Chen, Xin; Wolkowicz, Henry; Yuan, Yaxiang Strong duality for a trust-region type relaxation of the quadratic assignment problem. (English) Zbl 0953.90034 Linear Algebra Appl. 301, No. 1-3, 121-136 (1999). MSC: 90B80 90C22 90C20 PDFBibTeX XMLCite \textit{K. Anstreicher} et al., Linear Algebra Appl. 301, No. 1--3, 121--136 (1999; Zbl 0953.90034) Full Text: DOI
Singer, Ivan Duality for optimization and best approximation over finite intersections. (English) Zbl 0923.46071 Numer. Funct. Anal. Optimization 19, No. 7-8, 903-915 (1998). Reviewer: N.D.Sengupta (Bombay) MSC: 46N10 41A65 46B20 PDFBibTeX XMLCite \textit{I. Singer}, Numer. Funct. Anal. Optim. 19, No. 7--8, 903--915 (1998; Zbl 0923.46071) Full Text: DOI
Donagi, Ron Y. Seiberg-Witten integrable systems. (English) Zbl 0896.58057 Kollár, János (ed.) et al., Algebraic geometry. Proceedings of the Summer Research Institute, Santa Cruz, CA, USA, July 9–29, 1995. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 62(pt.2), 3-43 (1997). Reviewer: B.A.Malomed (Tel Aviv) MSC: 37K20 81R12 81T60 14H70 81T13 14D20 PDFBibTeX XMLCite \textit{R. Y. Donagi}, Proc. Symp. Pure Math. 62, 3--43 (1997; Zbl 0896.58057) Full Text: arXiv
Singh, C.; Bhatia, D.; Rueda, N. Duality in nonlinear multiobjective programming using augmented Lagrangian functions. (English) Zbl 0851.90107 J. Optimization Theory Appl. 88, No. 3, 659-670 (1996). MSC: 90C29 90C30 PDFBibTeX XMLCite \textit{C. Singh} et al., J. Optim. Theory Appl. 88, No. 3, 659--670 (1996; Zbl 0851.90107) Full Text: DOI
Tamminen, E. V. Sufficient conditions for the existence of multipliers and Lagrangian duality in abstract optimization problems. (English) Zbl 0824.49032 J. Optimization Theory Appl. 82, No. 1, 93-104 (1994). Reviewer: M.Gaviano (Cagliari) MSC: 49N15 90C48 90C30 PDFBibTeX XMLCite \textit{E. V. Tamminen}, J. Optim. Theory Appl. 82, No. 1, 93--104 (1994; Zbl 0824.49032) Full Text: DOI
Singer, Ivan Abstract subdifferentials and some characterizations of optimal solutions. (English) Zbl 0619.49007 J. Optimization Theory Appl. 57, No. 2, 361-368 (1988). MSC: 49N15 49J52 90C48 PDFBibTeX XMLCite \textit{I. Singer}, J. Optim. Theory Appl. 57, No. 2, 361--368 (1988; Zbl 0619.49007) Full Text: DOI
Passy, U.; Prisman, E. Z. A convex-like duality scheme for quasi-convex programs. (English) Zbl 0606.49009 Math. Program. 32, 278-300 (1985). Reviewer: G.Xue MSC: 49N15 26B25 90C25 PDFBibTeX XMLCite \textit{U. Passy} and \textit{E. Z. Prisman}, Math. Program. 32, 278--300 (1985; Zbl 0606.49009) Full Text: DOI
Zălinescu, Constantin Duality for vectorial nonconvex optimization by convexification and applications. (English) Zbl 0536.90073 An. Științ. Univ. Al. I. Cuza Iași, N. Ser., Secț. Ia 29, No. 3, Suppl., 15-34 (1983). Reviewer: B.Craven MSC: 90C31 90C48 49M37 90C30 PDFBibTeX XML
Hoffmann, A. Properties of a multiplier-multifunction. I. (English) Zbl 0523.49013 Wiss. Z. Tech. Hochsch. Ilmenau 29, No. 2, 39-46 (1983). MSC: 49N15 49J45 54C60 26E25 46B25 49J27 PDFBibTeX XMLCite \textit{A. Hoffmann}, Wiss. Z. Tech. Hochsch. Ilmenau 29, No. 2, 39--46 (1983; Zbl 0523.49013)
Zeidan, Vera Sufficient conditions for the generalized problem of Bolza. (English) Zbl 0649.49012 Seminarber. Fachber. Math., Fernuniv. Hagen 8, 161-209 (1981). MSC: 49K15 49L99 37J99 49J52 49N15 PDFBibTeX XML
Craven, B. D. Vector-valued optimization. (English) Zbl 0534.90080 Generalized concavity in optimization and economics, Proc. NATO Adv. Study Inst., Vancouver/Can. 1980, 661-687 (1981). MSC: 90C31 PDFBibTeX XML
Avriel, Mordecai Nonlinear programming. (English) Zbl 0498.90069 Mathematical programming for operations researchers and computer scientists, Ind. Eng. 6, 271-367 (1981). MSC: 90C30 90-02 65K05 PDFBibTeX XML
Reiland, Thomas W. Lagrangian duality for a class of infinite programming problems. (English) Zbl 0456.90087 Numer. Funct. Anal. Optimization 2, 507-530 (1980). MSC: 90C48 90C30 PDFBibTeX XMLCite \textit{T. W. Reiland}, Numer. Funct. Anal. Optim. 2, 507--530 (1980; Zbl 0456.90087) Full Text: DOI