Jia, Zhongxiao; Wang, Fa The convergence of the generalized Lanczos trust-region method for the trust-region subproblem. (English) Zbl 07330004 SIAM J. Optim. 31, No. 1, 887-914 (2021). MSC: 90C20 90C30 65K05 65F10 PDF BibTeX XML Cite \textit{Z. Jia} and \textit{F. Wang}, SIAM J. Optim. 31, No. 1, 887--914 (2021; Zbl 07330004) Full Text: DOI
Wang, Xiaohui; Zhang, Hao; Xia, Yong GPS localization problem: a new model and its global optimization. (English) Zbl 1452.90253 Optim. Eng. 21, No. 3, 851-866 (2020). MSC: 90C26 90C32 90C90 PDF BibTeX XML Cite \textit{X. Wang} et al., Optim. Eng. 21, No. 3, 851--866 (2020; Zbl 1452.90253) Full Text: DOI
Su, Ke; Wang, Chen; Li, Xiaochuan A modified nonmonotone filter method for minimax problems. (English) Zbl 07267263 Math. Appl. 33, No. 2, 358-372 (2020). MSC: 90C47 PDF BibTeX XML Cite \textit{K. Su} et al., Math. Appl. 33, No. 2, 358--372 (2020; Zbl 07267263)
Milz, Johannes; Ulbrich, Michael An approximation scheme for distributionally robust nonlinear optimization. (English) Zbl 1448.90068 SIAM J. Optim. 30, No. 3, 1996-2025 (2020). MSC: 90C17 90C26 90C46 90C59 49M37 PDF BibTeX XML Cite \textit{J. Milz} and \textit{M. Ulbrich}, SIAM J. Optim. 30, No. 3, 1996--2025 (2020; Zbl 1448.90068) Full Text: DOI
Wang, Jiulin; Xia, Yong Closing the gap between necessary and sufficient conditions for local nonglobal minimizer of trust region subproblem. (English) Zbl 07236496 SIAM J. Optim. 30, No. 3, 1980-1995 (2020). MSC: 90C20 90C26 90C30 90C46 PDF BibTeX XML Cite \textit{J. Wang} and \textit{Y. Xia}, SIAM J. Optim. 30, No. 3, 1980--1995 (2020; Zbl 07236496) Full Text: DOI
Liu, Ji-Chuan; Li, Xiao-Chen Reconstruction algorithms of an inverse source problem for the Helmholtz equation. (English) Zbl 1442.65334 Numer. Algorithms 84, No. 3, 909-933 (2020). MSC: 65N21 65N20 65J20 65K10 35R30 35J05 35R25 PDF BibTeX XML Cite \textit{J.-C. Liu} and \textit{X.-C. Li}, Numer. Algorithms 84, No. 3, 909--933 (2020; Zbl 1442.65334) Full Text: DOI
Brás, C. P.; Martínez, J. M.; Raydan, M. Large-scale unconstrained optimization using separable cubic modeling and matrix-free subspace minimization. (English) Zbl 1432.90119 Comput. Optim. Appl. 75, No. 1, 169-205 (2020). MSC: 90C26 65K10 90C06 PDF BibTeX XML Cite \textit{C. P. Brás} et al., Comput. Optim. Appl. 75, No. 1, 169--205 (2020; Zbl 1432.90119) Full Text: DOI
Liu, Ji-Chuan Reconstruction algorithms of an inverse geometric problem for the modified Helmholtz equation. (English) Zbl 1438.65278 Comput. Appl. Math. 38, No. 4, Paper No. 167, 18 p. (2019). MSC: 65N20 65N21 35J05 35R30 PDF BibTeX XML Cite \textit{J.-C. Liu}, Comput. Appl. Math. 38, No. 4, Paper No. 167, 18 p. (2019; Zbl 1438.65278) Full Text: DOI
Youett, Jonathan; Sander, Oliver; Kornhuber, Ralf A globally convergent filter-trust-region method for large deformation contact problems. (English) Zbl 1414.65045 SIAM J. Sci. Comput. 41, No. 1, B114-B138 (2019). Reviewer: Marius Ghergu (Dublin) MSC: 65N55 65K15 65N30 65N12 74B20 74M15 PDF BibTeX XML Cite \textit{J. Youett} et al., SIAM J. Sci. Comput. 41, No. 1, B114--B138 (2019; Zbl 1414.65045) Full Text: DOI arXiv
El-Sobky, Bothina; Abotahoun, Abdallah A trust-region algorithm for solving mini-max problem. (English) Zbl 1424.65081 J. Comput. Math. 36, No. 6, 776-791 (2018). MSC: 65K05 90C47 PDF BibTeX XML Cite \textit{B. El-Sobky} and \textit{A. Abotahoun}, J. Comput. Math. 36, No. 6, 776--791 (2018; Zbl 1424.65081) Full Text: DOI
EL-Sobky, B.; Aboutahoun, A. W. An active-set algorithm and a trust-region approach in constrained minimax problem. (English) Zbl 1406.49035 Comput. Appl. Math. 37, No. 3, 2605-2631 (2018). Reviewer: Zhang Xian (Xiamen) MSC: 49N35 49N10 49J35 65K05 90C47 PDF BibTeX XML Cite \textit{B. EL-Sobky} and \textit{A. W. Aboutahoun}, Comput. Appl. Math. 37, No. 3, 2605--2631 (2018; Zbl 1406.49035) Full Text: DOI
Salahi, M.; Taati, A. A fast eigenvalue approach for solving the trust region subproblem with an additional linear inequality. (English) Zbl 1393.90097 Comput. Appl. Math. 37, No. 1, 329-347 (2018). MSC: 90C26 90C22 65F15 PDF BibTeX XML Cite \textit{M. Salahi} and \textit{A. Taati}, Comput. Appl. Math. 37, No. 1, 329--347 (2018; Zbl 1393.90097) Full Text: DOI
Liu, Ji-Chuan Reconstruction algorithms for an inverse medium problem. (English) Zbl 06890305 Appl. Math., Praha 63, No. 2, 195-216 (2018). MSC: 65N20 65N21 PDF BibTeX XML Cite \textit{J.-C. Liu}, Appl. Math., Praha 63, No. 2, 195--216 (2018; Zbl 06890305) Full Text: DOI
El-Sobky, B.; Abo-Elnaga, Y. A penalty method with trust-region mechanism for nonlinear bilevel optimization problem. (English) Zbl 1391.90572 J. Comput. Appl. Math. 340, 360-374 (2018). MSC: 90C30 90B50 65K05 62C20 PDF BibTeX XML Cite \textit{B. El-Sobky} and \textit{Y. Abo-Elnaga}, J. Comput. Appl. Math. 340, 360--374 (2018; Zbl 1391.90572) Full Text: DOI
Galli, Leonardo; Kanzow, Christian; Sciandrone, Marco A nonmonotone trust-region method for generalized Nash equilibrium and related problems with strong convergence properties. (English) Zbl 1390.90515 Comput. Optim. Appl. 69, No. 3, 629-652 (2018). MSC: 90C30 65H10 PDF BibTeX XML Cite \textit{L. Galli} et al., Comput. Optim. Appl. 69, No. 3, 629--652 (2018; Zbl 1390.90515) Full Text: DOI
Liu, Ji-Chuan An inverse source problem of the Poisson equation with Cauchy data. (English) Zbl 1372.65296 Electron. J. Differ. Equ. 2017, Paper No. 119, 19 p. (2017). MSC: 65N20 65N21 PDF BibTeX XML Cite \textit{J.-C. Liu}, Electron. J. Differ. Equ. 2017, Paper No. 119, 19 p. (2017; Zbl 1372.65296) Full Text: Link
Wang, Yi-Ju; Zhou, Guang-Lu A hybrid second-order method for homogenous polynomial optimization over unit sphere. (English) Zbl 1371.65036 J. Oper. Res. Soc. China 5, No. 1, 99-109 (2017). MSC: 65F15 65K05 90C51 PDF BibTeX XML Cite \textit{Y.-J. Wang} and \textit{G.-L. Zhou}, J. Oper. Res. Soc. China 5, No. 1, 99--109 (2017; Zbl 1371.65036) Full Text: DOI
Su, Ke; Lu, Mingxi An improved ODE-type filter method for nonlinear complementarity problem. (English) Zbl 1371.90130 Far East J. Appl. Math. 96, No. 1, 1-16 (2017). MSC: 90C30 PDF BibTeX XML Cite \textit{K. Su} and \textit{M. Lu}, Far East J. Appl. Math. 96, No. 1, 1--16 (2017; Zbl 1371.90130) Full Text: DOI Link
Muoi, Bui Ngoc; Yen, Nguyen Dong Local stability and local convergence of the basic trust-region method. (English) Zbl 1372.90104 J. Optim. Theory Appl. 172, No. 2, 578-593 (2017). MSC: 90C30 90C26 49M37 PDF BibTeX XML Cite \textit{B. N. Muoi} and \textit{N. D. Yen}, J. Optim. Theory Appl. 172, No. 2, 578--593 (2017; Zbl 1372.90104) Full Text: DOI
Saeidian, Z.; Reza Peyghami, M.; Habibi, M.; Ghasemi, S. A new trust-region method for solving systems of equalities and inequalities. (English) Zbl 1359.65095 Comput. Appl. Math. 36, No. 1, 769-790 (2017). MSC: 65K05 90C30 PDF BibTeX XML Cite \textit{Z. Saeidian} et al., Comput. Appl. Math. 36, No. 1, 769--790 (2017; Zbl 1359.65095) Full Text: DOI
Curtis, Frank E.; Robinson, Daniel P.; Samadi, Mohammadreza A trust region algorithm with a worst-case iteration complexity of \(\mathcal{O}(\epsilon ^{-3/2})\) for nonconvex optimization. (English) Zbl 1360.49020 Math. Program. 162, No. 1-2 (A), 1-32 (2017). MSC: 49M15 49M37 58C15 65K05 65K10 65Y20 68Q25 90C30 90C60 PDF BibTeX XML Cite \textit{F. E. Curtis} et al., Math. Program. 162, No. 1--2 (A), 1--32 (2017; Zbl 1360.49020) Full Text: DOI
Salahi, Maziar; Taati, Akram; Wolkowicz, Henry Local nonglobal minima for solving large-scale extended trust-region subproblems. (English) Zbl 1391.90496 Comput. Optim. Appl. 66, No. 2, 223-244 (2017). MSC: 90C26 90C30 90C46 65F15 PDF BibTeX XML Cite \textit{M. Salahi} et al., Comput. Optim. Appl. 66, No. 2, 223--244 (2017; Zbl 1391.90496) Full Text: DOI arXiv
Adachi, Satoru; Iwata, Satoru; Nakatsukasa, Yuji; Takeda, Akiko Solving the trust-region subproblem by a generalized eigenvalue problem. (English) Zbl 1359.49009 SIAM J. Optim. 27, No. 1, 269-291 (2017). MSC: 49M37 65K10 90C25 90C30 PDF BibTeX XML Cite \textit{S. Adachi} et al., SIAM J. Optim. 27, No. 1, 269--291 (2017; Zbl 1359.49009) Full Text: DOI
Francisco, J. B.; Viloche Bazán, F. S.; Weber Mendonça, M. Non-monotone algorithm for minimization on arbitrary domains with applications to large-scale orthogonal Procrustes problem. (English) Zbl 1354.65120 Appl. Numer. Math. 112, 51-64 (2017). MSC: 65K05 90C30 90C51 PDF BibTeX XML Cite \textit{J. B. Francisco} et al., Appl. Numer. Math. 112, 51--64 (2017; Zbl 1354.65120) Full Text: DOI
Grapiglia, Geovani Nunes; Yuan, Jinyun; Yuan, Ya-xiang A derivative-free trust-region algorithm for composite nonsmooth optimization. (English) Zbl 1371.49014 Comput. Appl. Math. 35, No. 2, 475-499 (2016). MSC: 49J53 90C30 58C15 49M37 90C56 68Q25 65K05 49J52 PDF BibTeX XML Cite \textit{G. N. Grapiglia} et al., Comput. Appl. Math. 35, No. 2, 475--499 (2016; Zbl 1371.49014) Full Text: DOI
Bernal, Francisco Trust-region methods for nonlinear elliptic equations with radial basis functions. (English) Zbl 1361.65092 Comput. Math. Appl. 72, No. 7, 1743-1763 (2016). MSC: 65N35 35J60 35J61 35J62 35J96 PDF BibTeX XML Cite \textit{F. Bernal}, Comput. Math. Appl. 72, No. 7, 1743--1763 (2016; Zbl 1361.65092) Full Text: DOI arXiv
Xie, Dongxiu; Xu, An-Bao; Peng, Zhenyun Least-squares symmetric solution to the matrix equation \(AXB=C\) with the norm inequality constraint. (English) Zbl 1360.65131 Int. J. Comput. Math. 93, No. 9, 1564-1578 (2016). Reviewer: Constantin Popa (Constanţa) MSC: 65F30 65F10 15A24 65F20 PDF BibTeX XML Cite \textit{D. Xie} et al., Int. J. Comput. Math. 93, No. 9, 1564--1578 (2016; Zbl 1360.65131) Full Text: DOI
Grapiglia, Geovani Nunes; Yuan, Jinyun; Yuan, Ya-xiang Nonlinear stepsize control algorithms: complexity bounds for first- and second-order optimality. (English) Zbl 1354.90138 J. Optim. Theory Appl. 171, No. 3, 980-997 (2016). MSC: 90C30 65K05 49M37 49M15 90C29 90C60 68Q25 PDF BibTeX XML Cite \textit{G. N. Grapiglia} et al., J. Optim. Theory Appl. 171, No. 3, 980--997 (2016; Zbl 1354.90138) Full Text: DOI
Xu, Wei; Zheng, Ning; Hayami, Ken Jacobian-free implicit inner-iteration preconditioner for nonlinear least squares problems. (English) Zbl 1352.65158 J. Sci. Comput. 68, No. 3, 1055-1081 (2016). MSC: 65K05 90C20 65D25 90C51 90C53 65F08 PDF BibTeX XML Cite \textit{W. Xu} et al., J. Sci. Comput. 68, No. 3, 1055--1081 (2016; Zbl 1352.65158) Full Text: DOI
Locatelli, Marco Exactness conditions for an SDP relaxation of the extended trust region problem. (English) Zbl 1353.90102 Optim. Lett. 10, No. 6, 1141-1151 (2016). MSC: 90C20 PDF BibTeX XML Cite \textit{M. Locatelli}, Optim. Lett. 10, No. 6, 1141--1151 (2016; Zbl 1353.90102) Full Text: DOI
Zeng, Meilan; Zhou, Guanghui A trust region spectral method for large-scale systems of nonlinear equations. (English) Zbl 1343.65061 J. Inequal. Appl. 2016, Paper No. 174, 12 p. (2016). MSC: 65H10 PDF BibTeX XML Cite \textit{M. Zeng} and \textit{G. Zhou}, J. Inequal. Appl. 2016, Paper No. 174, 12 p. (2016; Zbl 1343.65061) Full Text: DOI
Yuan, JianHua; Wang, MeiLing; Ai, WenBao; Shuai, TianPing A necessary and sufficient condition of convexity for SOC reformulation of trust-region subproblem with two intersecting cuts. (English) Zbl 1344.49040 Sci. China, Math. 59, No. 6, 1127-1140 (2016). MSC: 49K21 49M37 49M20 90C20 90C22 90C25 90C26 90C30 PDF BibTeX XML Cite \textit{J. Yuan} et al., Sci. China, Math. 59, No. 6, 1127--1140 (2016; Zbl 1344.49040) Full Text: DOI
Bomze, Immanuel M. Copositivity for second-order optimality conditions in general smooth optimization problems. (English) Zbl 1384.90074 Optimization 65, No. 4, 779-795 (2016). MSC: 90C26 90C46 90C56 PDF BibTeX XML Cite \textit{I. M. Bomze}, Optimization 65, No. 4, 779--795 (2016; Zbl 1384.90074) Full Text: DOI
Dymarsky, Anatoly Convexity of a small ball under quadratic map. (English) Zbl 1327.15046 Linear Algebra Appl. 488, 109-123 (2016). MSC: 15A60 15A22 52A20 PDF BibTeX XML Cite \textit{A. Dymarsky}, Linear Algebra Appl. 488, 109--123 (2016; Zbl 1327.15046) Full Text: DOI arXiv
Nino Ruiz, Elias D.; Sandu, Adrian A derivative-free trust region framework for variational data assimilation. (English) Zbl 1326.65070 J. Comput. Appl. Math. 293, 164-179 (2016). MSC: 65K05 68Q10 86A10 90C15 90C51 90C59 65C05 PDF BibTeX XML Cite \textit{E. D. Nino Ruiz} and \textit{A. Sandu}, J. Comput. Appl. Math. 293, 164--179 (2016; Zbl 1326.65070) Full Text: DOI
Grapiglia, Geovani N.; Yuan, Jinyun; Yuan, Ya-xiang On the convergence and worst-case complexity of trust-region and regularization methods for unconstrained optimization. (English) Zbl 1319.90065 Math. Program. 152, No. 1-2 (A), 491-520 (2015). MSC: 90C30 65K05 49M37 49M15 90C29 90C60 68Q25 PDF BibTeX XML Cite \textit{G. N. Grapiglia} et al., Math. Program. 152, No. 1--2 (A), 491--520 (2015; Zbl 1319.90065) Full Text: DOI
Arouxét, Ma. Belén; Echebest, Nélida E.; Pilotta, Elvio A. Inexact restoration method for nonlinear optimization without derivatives. (English) Zbl 1321.65093 J. Comput. Appl. Math. 290, 26-43 (2015). MSC: 65K05 90C30 90C51 90C56 PDF BibTeX XML Cite \textit{Ma. B. Arouxét} et al., J. Comput. Appl. Math. 290, 26--43 (2015; Zbl 1321.65093) Full Text: DOI
Bomze, Immanuel M.; Overton, Michael L. Narrowing the difficulty gap for the Celis-Dennis-Tapia problem. (English) Zbl 1328.90095 Math. Program. 151, No. 2 (B), 459-476 (2015). MSC: 90C20 90C26 PDF BibTeX XML Cite \textit{I. M. Bomze} and \textit{M. L. Overton}, Math. Program. 151, No. 2 (B), 459--476 (2015; Zbl 1328.90095) Full Text: DOI
Long, Jun; Zeng, Sanyun A trust region-SQP-filter algorithm for solving nonlinear complementarity problem. (Chinese. English summary) Zbl 1340.90246 J. Huaihua Univ. 33, No. 5, 13-16 (2014). MSC: 90C33 90C30 PDF BibTeX XML Cite \textit{J. Long} and \textit{S. Zeng}, J. Huaihua Univ. 33, No. 5, 13--16 (2014; Zbl 1340.90246)
Long, Jun; Zeng, Sanyun A filter interior-point algorithm for nonlinear complementarity problems. (Chinese. English summary) Zbl 1313.65152 Pure Appl. Math. 30, No. 3, 245-254 (2014). MSC: 65K05 90C33 90C30 90C51 PDF BibTeX XML Cite \textit{J. Long} and \textit{S. Zeng}, Pure Appl. Math. 30, No. 3, 245--254 (2014; Zbl 1313.65152) Full Text: DOI
Ji, Ying; Wang, Tienan; Li, Yijun; Zhou, Yong A new smoothing nonmonotone trust region method for solving nonlinear complementarity problems. (English) Zbl 1338.90409 Adv. Appl. Stat. 40, No. 1, 31-60 (2014). MSC: 90C33 90C26 90C30 PDF BibTeX XML Cite \textit{Y. Ji} et al., Adv. Appl. Stat. 40, No. 1, 31--60 (2014; Zbl 1338.90409) Full Text: Link
Lombera, Hassán; Tello, J. Ignacio A numerical approach to solve an inverse problem in lubrication theory. (English) Zbl 1432.65140 Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 108, No. 2, 617-631 (2014). MSC: 65M32 65M60 76D08 PDF BibTeX XML Cite \textit{H. Lombera} and \textit{J. I. Tello}, Rev. R. Acad. Cienc. Exactas Fís. Nat., Ser. A Mat., RACSAM 108, No. 2, 617--631 (2014; Zbl 1432.65140) Full Text: DOI
Gumma, E. A. E.; Hashim, M. H. A.; Ali, M. Montaz A derivative-free algorithm for linearly constrained optimization problems. (English) Zbl 1304.90193 Comput. Optim. Appl. 57, No. 3, 599-621 (2014). MSC: 90C30 90C56 PDF BibTeX XML Cite \textit{E. A. E. Gumma} et al., Comput. Optim. Appl. 57, No. 3, 599--621 (2014; Zbl 1304.90193) Full Text: DOI
Zhang, Lei-Hong On a self-consistent-field-like iteration for maximizing the sum of the Rayleigh quotients. (English) Zbl 1294.65065 J. Comput. Appl. Math. 257, 14-28 (2014). MSC: 65K05 90C20 90C51 65H17 62H30 68T10 PDF BibTeX XML Cite \textit{L.-H. Zhang}, J. Comput. Appl. Math. 257, 14--28 (2014; Zbl 1294.65065) Full Text: DOI
Villacorta, Kely D. V.; Oliveira, Paulo R.; Soubeyran, Antoine A trust-region method for unconstrained multiobjective problems with applications in satisficing processes. (English) Zbl 1300.90045 J. Optim. Theory Appl. 160, No. 3, 865-889 (2014). MSC: 90C29 PDF BibTeX XML Cite \textit{K. D. V. Villacorta} et al., J. Optim. Theory Appl. 160, No. 3, 865--889 (2014; Zbl 1300.90045) Full Text: DOI
Renka, Robert J. A trust region method for constructing triangle-mesh approximations of parametric minimal surfaces. (English) Zbl 1288.65023 Appl. Numer. Math. 76, 93-100 (2014). MSC: 65D17 65K05 90C51 53A10 49Q05 PDF BibTeX XML Cite \textit{R. J. Renka}, Appl. Numer. Math. 76, 93--100 (2014; Zbl 1288.65023) Full Text: DOI
Gibali, A.; Küfer, K.-H.; Süss, P. Successive linear programming approach for solving the nonlinear split feasibility problem. (Successive linear programing approach for solving the nonlinear split feasibility problem.) (English) Zbl 1291.90171 J. Nonlinear Convex Anal. 15, No. 2, 345-353 (2014). Reviewer: K. C. Sivakumar (Chennai) MSC: 90C25 47J25 47H05 47H09 47J20 90C05 PDF BibTeX XML Cite \textit{A. Gibali} et al., J. Nonlinear Convex Anal. 15, No. 2, 345--353 (2014; Zbl 1291.90171) Full Text: Link
Quarteroni, Alfio; Saleri, Fausto; Gervasio, Paola Scientific computing with MATLAB and Octave. 4th ed. (English) Zbl 1306.65001 Texts in Computational Science and Engineering 2. Berlin: Springer (ISBN 978-3-642-45366-3/hbk; 978-3-642-45367-0/ebook). xviii, 442 p. (2014). Reviewer: Robert Plato (Siegen) MSC: 65-01 65B05 65Dxx 65F05 65F10 65F15 65K10 65Lxx 65N06 65N30 65Yxx PDF BibTeX XML Cite \textit{A. Quarteroni} et al., Scientific computing with MATLAB and Octave. 4th ed. Berlin: Springer (2014; Zbl 1306.65001) Full Text: DOI
Wang, Fu-Sheng; Wang, Chuan-Long An adaptive nonmonotone trust-region method with curvilinear search for minimax problem. (English) Zbl 1366.90220 Appl. Math. Comput. 219, No. 15, 8033-8041 (2013). MSC: 90C47 65K05 PDF BibTeX XML Cite \textit{F.-S. Wang} and \textit{C.-L. Wang}, Appl. Math. Comput. 219, No. 15, 8033--8041 (2013; Zbl 1366.90220) Full Text: DOI
Min, Tao; Zhao, Miaomiao; Hu, Gang A regularization GMRES method for solving the Symm integral equation. (Chinese. English summary) Zbl 1289.65293 Chin. J. Eng. Math. 30, No. 2, 271-277 (2013). MSC: 65R20 45B05 65F10 65R30 PDF BibTeX XML Cite \textit{T. Min} et al., Chin. J. Eng. Math. 30, No. 2, 271--277 (2013; Zbl 1289.65293) Full Text: DOI
Wang, Yunjuan; Zhu, Detong An affine scaling interior trust region method for variational inequality problems. (English) Zbl 1289.90237 J. Math., Wuhan Univ. 33, No. 1, 35-50 (2013). MSC: 90C33 90C51 90C30 65K05 PDF BibTeX XML Cite \textit{Y. Wang} and \textit{D. Zhu}, J. Math., Wuhan Univ. 33, No. 1, 35--50 (2013; Zbl 1289.90237)
Pištěk, Miroslav Approximate dynamic programming based on high dimensional model representation. (English) Zbl 1278.90423 Kybernetika 49, No. 5, 720-737 (2013). MSC: 90C39 PDF BibTeX XML Cite \textit{M. Pištěk}, Kybernetika 49, No. 5, 720--737 (2013; Zbl 1278.90423) Full Text: Link arXiv
Liu, Guo-shan; Xu, Shi-qin; Han, Ji-ye A trust region algorithm for solving bilevel programming problems. (English) Zbl 1277.90101 Acta Math. Appl. Sin., Engl. Ser. 29, No. 3, 491-498 (2013). MSC: 90C26 91B02 PDF BibTeX XML Cite \textit{G.-s. Liu} et al., Acta Math. Appl. Sin., Engl. Ser. 29, No. 3, 491--498 (2013; Zbl 1277.90101) Full Text: DOI
Bucher, Anke; Görke, Uwe-Jens; Kreißig, Reiner Towards the direct and inverse adaptive mixed finite element formulations for nearly incompressible elasticity at large strains. (English) Zbl 1410.74060 Apel, Thomas (ed.) et al., Advanced finite element methods and applications. Berlin: Springer. Lect. Notes Appl. Comput. Mech. 66, 299-323 (2013). MSC: 74S05 74B20 74G75 74K15 PDF BibTeX XML Cite \textit{A. Bucher} et al., Lect. Notes Appl. Comput. Mech. 66, 299--323 (2013; Zbl 1410.74060) Full Text: DOI
Martin, David R.; Reichel, Lothar Minimization of functionals on the solution of a large-scale discrete ill-posed problem. (English) Zbl 1262.65053 BIT 53, No. 1, 153-173 (2013). MSC: 65F22 65K05 90C05 90C06 PDF BibTeX XML Cite \textit{D. R. Martin} and \textit{L. Reichel}, BIT 53, No. 1, 153--173 (2013; Zbl 1262.65053) Full Text: DOI
Zhang, Lei-Hong On optimizing the sum of the Rayleigh quotient and the generalized Rayleigh quotient on the unit sphere. (English) Zbl 1285.90042 Comput. Optim. Appl. 54, No. 1, 111-139 (2013). MSC: 90C26 PDF BibTeX XML Cite \textit{L.-H. Zhang}, Comput. Optim. Appl. 54, No. 1, 111--139 (2013; Zbl 1285.90042) Full Text: DOI
Renka, Robert J. Nonlinear least squares and Sobolev gradients. (English) Zbl 1260.65060 Appl. Numer. Math. 65, 91-104 (2013). MSC: 65K10 49J15 49M15 PDF BibTeX XML Cite \textit{R. J. Renka}, Appl. Numer. Math. 65, 91--104 (2013; Zbl 1260.65060) Full Text: DOI
Liu, Jinghui; Ma, Changfeng A new non-monotone trust region algorithm for solving unconstrained optimization problems. (Chinese. English summary) Zbl 1289.90198 J. Fujian Norm. Univ., Nat. Sci. 28, No. 3, 19-25 (2012). MSC: 90C30 65K05 49M37 PDF BibTeX XML Cite \textit{J. Liu} and \textit{C. Ma}, J. Fujian Norm. Univ., Nat. Sci. 28, No. 3, 19--25 (2012; Zbl 1289.90198)
Lantoine, Gregory; Russell, Ryan P. A hybrid differential dynamic programming algorithm for constrained optimal control problems. I: Theory. (English) Zbl 1260.49044 J. Optim. Theory Appl. 154, No. 2, 382-417 (2012). Reviewer: Joseph Frédéric Bonnans (Le Chesnay) MSC: 49L20 90C06 90C20 90C39 PDF BibTeX XML Cite \textit{G. Lantoine} and \textit{R. P. Russell}, J. Optim. Theory Appl. 154, No. 2, 382--417 (2012; Zbl 1260.49044) Full Text: DOI
El-Sobky, Bothina; Abo-Elnaga, Yousria An active-set trust-region algorithm for solving constrained multi-objective optimization problem. (English) Zbl 1246.90133 Appl. Math. Sci., Ruse 6, No. 33-36, 1599-1612 (2012). MSC: 90C29 PDF BibTeX XML Cite \textit{B. El-Sobky} and \textit{Y. Abo-Elnaga}, Appl. Math. Sci., Ruse 6, No. 33--36, 1599--1612 (2012; Zbl 1246.90133) Full Text: Link
Chen, X.; Akella, S.; Navon, I. M. A dual-weighted trust-region adaptive POD 4-D var applied to a finite-volume shallow water equations model on the sphere. (English) Zbl 1426.76347 Int. J. Numer. Methods Fluids 68, No. 3, 377-402 (2012). MSC: 76M12 76U05 86A05 PDF BibTeX XML Cite \textit{X. Chen} et al., Int. J. Numer. Methods Fluids 68, No. 3, 377--402 (2012; Zbl 1426.76347) Full Text: DOI
Mombaur, Katja; Laumond, Jean-Paul; Truong, Anh An inverse optimal control approach to human motion modeling. (English) Zbl 1250.49037 Pradalier, Cédric (ed.) et al., Robotics research. The 14th international symposium ISRR. Selected papers based on the presentations at the symposium, Lucerne, Switzerland, August 31st to September 3rd, 2009. Berlin: Springer (ISBN 978-3-642-19456-6/hbk; 978-3-642-19457-3/ebook). Springer Tracts in Advanced Robotics 70, 451-468 (2011). MSC: 49N45 49N90 93A30 49M30 93C85 PDF BibTeX XML Cite \textit{K. Mombaur} et al., Springer Tracts Adv. Robot. 70, 451--468 (2011; Zbl 1250.49037) Full Text: DOI
Wang, Xuebin; Ma, Changfeng; Li, Meiyan A smoothing trust region method for NCPS based on the smoothing generalized Fischer-Burmeister function. (English) Zbl 1249.90289 J. Comput. Math. 29, No. 3, 261-286 (2011). MSC: 90C33 PDF BibTeX XML Cite \textit{X. Wang} et al., J. Comput. Math. 29, No. 3, 261--286 (2011; Zbl 1249.90289) Full Text: DOI
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. On the evaluation complexity of composite function minimization with applications to nonconvex nonlinear programming. (English) Zbl 1236.90118 SIAM J. Optim. 21, No. 4, 1721-1739 (2011). MSC: 90C30 90C26 65K05 49M05 49M37 58C15 90C60 68Q25 PDF BibTeX XML Cite \textit{C. Cartis} et al., SIAM J. Optim. 21, No. 4, 1721--1739 (2011; Zbl 1236.90118) Full Text: DOI
Zhou, Qian; Ou, Yi-Gui A hybrid method for NCP with \(P_0\) functions. (English) Zbl 1235.90164 J. Appl. Math. Inform. 29, No. 3-4, 653-668 (2011). MSC: 90C33 90C30 65H10 PDF BibTeX XML Cite \textit{Q. Zhou} and \textit{Y.-G. Ou}, J. Appl. Math. Inform. 29, No. 3--4, 653--668 (2011; Zbl 1235.90164)
Cartis, Coralia; Gould, Nicholas I. M.; Toint, Philippe L. Adaptive cubic regularisation methods for unconstrained optimization. II: Worst-case function- and derivative-evaluation complexity. (English) Zbl 1229.90193 Math. Program. 130, No. 2 (A), 295-319 (2011). MSC: 90C30 65K05 49M37 49M15 58C15 90C60 68Q25 PDF BibTeX XML Cite \textit{C. Cartis} et al., Math. Program. 130, No. 2 (A), 295--319 (2011; Zbl 1229.90193) Full Text: DOI
Chen, X.; Navon, I. M.; Fang, F. A dual-weighted trust-region adaptive POD 4D-VAR applied to a finite-element shallow-water equations model. (English) Zbl 1428.76145 Int. J. Numer. Methods Fluids 65, No. 5, 520-541 (2011). MSC: 76M21 76M10 35Q35 PDF BibTeX XML Cite \textit{X. Chen} et al., Int. J. Numer. Methods Fluids 65, No. 5, 520--541 (2011; Zbl 1428.76145) Full Text: DOI
Li, Meiyan; Ma, Changfeng A nonmonotone adaptive trust region method for nonlinear complementarity problems. (Chinese. English summary) Zbl 1240.90438 J. Anhui Univ., Nat. Sci. 34, No. 3, 32-37 (2010). MSC: 90C33 65K05 PDF BibTeX XML Cite \textit{M. Li} and \textit{C. Ma}, J. Anhui Univ., Nat. Sci. 34, No. 3, 32--37 (2010; Zbl 1240.90438)
Cartis, C.; Gould, N. I. M.; Toint, Ph. L. On the complexity of steepest descent, Newton’s and regularized Newton’s methods for nonconvex unconstrained optimization problems. (English) Zbl 1211.90225 SIAM J. Optim. 20, No. 6, 2833-2852 (2010). MSC: 90C30 65K05 49M37 49M15 49M05 58C15 90C60 68Q25 PDF BibTeX XML Cite \textit{C. Cartis} et al., SIAM J. Optim. 20, No. 6, 2833--2852 (2010; Zbl 1211.90225) Full Text: DOI
Groß, Christian; Krause, Rolf A recursive trust-region method for non-convex constrained minimization. (English) Zbl 1183.65077 Bercovier, Michel (ed.) et al., Domain decomposition methods in science and engineering XVIII. Selected papers based on the presentations at the 18th international conference of domain decomposition methods, Jerusalem, Israel, January 12–17, 2008. Berlin: Springer (ISBN 978-3-642-02676-8/hbk; 978-3-642-04466-3/ebook). Lecture Notes in Computational Science and Engineering 70, 137-144 (2009). MSC: 65K10 49J20 49M37 90C51 PDF BibTeX XML Cite \textit{C. Groß} and \textit{R. Krause}, Lect. Notes Comput. Sci. Eng. 70, 137--144 (2009; Zbl 1183.65077) Full Text: DOI
Bellavia, Stefania; Pieraccini, Sandra Numerical solution of KKT systems in PDE-constrained optimization problems via the affine scaling trust-region approach. (English) Zbl 1181.65093 Int. J. Comput. Math. 86, No. 12, 2122-2142 (2009). MSC: 65K10 49J20 49M37 90C51 PDF BibTeX XML Cite \textit{S. Bellavia} and \textit{S. Pieraccini}, Int. J. Comput. Math. 86, No. 12, 2122--2142 (2009; Zbl 1181.65093) Full Text: DOI
Zhou, Ying A smoothing conic trust region filter method for the nonlinear complementarity problem. (English) Zbl 1167.65037 J. Comput. Appl. Math. 229, No. 1, 248-263 (2009). Reviewer: Hang Lau (Montréal) MSC: 65K05 90C33 90C51 PDF BibTeX XML Cite \textit{Y. Zhou}, J. Comput. Appl. Math. 229, No. 1, 248--263 (2009; Zbl 1167.65037) Full Text: DOI
Xue, Wenjuan; Shen, Chungen; Pu, Dingguo A penalty-function-free line search SQP method for nonlinear programming. (English) Zbl 1169.65060 J. Comput. Appl. Math. 228, No. 1, 313-325 (2009). Reviewer: Karel Zimmermann (Praha) MSC: 65K05 90C30 90C20 90C55 90C51 PDF BibTeX XML Cite \textit{W. Xue} et al., J. Comput. Appl. Math. 228, No. 1, 313--325 (2009; Zbl 1169.65060) Full Text: DOI
Lukšan, Ladislav; Matonoha, Ctirad; Vlček, Jan On Lagrange multipliers of trust-region subproblems. (English) Zbl 1203.65092 Chleboun, J. (ed.) et al., Programs and algorithms of numerical mathematics 14. Proceedings of the seminar, Dolní Maxov, Czech Republic, June 1–6, 2008. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics (ISBN 978-80-85823-55-4). 130-137 (2008). MSC: 65K05 90C30 90C51 90C06 PDF BibTeX XML Cite \textit{L. Lukšan} et al., in: Programs and algorithms of numerical mathematics 14. Proceedings of the seminar, Dolní\ Maxov, Czech Republic, June 1--6, 2008. Prague: Academy of Sciences of the Czech Republic, Institute of Mathematics. 130--137 (2008; Zbl 1203.65092)
Li, Zhuang; Han, Bo An adaptive homotopy inversion algorithm for 2-D GPR problems. (Chinese. English summary) Zbl 1199.65322 Period. Ocean Univ. China 38, No. 4, 685-688 (2008). MSC: 65M32 65H20 86A22 90C51 35R30 PDF BibTeX XML Cite \textit{Z. Li} and \textit{B. Han}, Period. Ocean Univ. China 38, No. 4, 685--688 (2008; Zbl 1199.65322)
Beck, Amir; Teboulle, Marc; Chikishev, Zahar Iterative minimization schemes for solving the single source localization problem. (English) Zbl 1180.90242 SIAM J. Optim. 19, No. 3, 1397-1416 (2008). MSC: 90C26 90C22 90C90 PDF BibTeX XML Cite \textit{A. Beck} et al., SIAM J. Optim. 19, No. 3, 1397--1416 (2008; Zbl 1180.90242) Full Text: DOI
Wang, Fusheng; Zhang, Kecun A hybrid algorithm for nonlinear minimax problems. (English) Zbl 1171.90544 Ann. Oper. Res. 164, 167-191 (2008). MSC: 90C47 PDF BibTeX XML Cite \textit{F. Wang} and \textit{K. Zhang}, Ann. Oper. Res. 164, 167--191 (2008; Zbl 1171.90544) Full Text: DOI
Wang, Yunjuan; Zhu, Detong An affine scaling interior trust region-type method for solving monotone variational inequality problem. (English) Zbl 1174.49316 OR Trans. 12, No. 3, 35-49 (2008). MSC: 49M15 49J40 90C51 65K10 PDF BibTeX XML Cite \textit{Y. Wang} and \textit{D. Zhu}, OR Trans. 12, No. 3, 35--49 (2008; Zbl 1174.49316)
Chen, Weimin; Yang, Yufei Smoothing methods for solving general nonlinear complementarity problems. (Chinese. English summary) Zbl 1174.90791 OR Trans. 12, No. 1, 93-103 (2008). MSC: 90C30 90C33 PDF BibTeX XML Cite \textit{W. Chen} and \textit{Y. Yang}, OR Trans. 12, No. 1, 93--103 (2008; Zbl 1174.90791)
Liu, Xin; Yuan, Yaxiang On the separable nonlinear least squares problems. (English) Zbl 1174.65021 J. Comput. Math. 26, No. 3, 390-403 (2008). MSC: 65K05 90C20 90C51 PDF BibTeX XML Cite \textit{X. Liu} and \textit{Y. Yuan}, J. Comput. Math. 26, No. 3, 390--403 (2008; Zbl 1174.65021)
Baker, C. G.; Absil, P.-A.; Gallivan, K. A. An implicit trust-region method on Riemannian manifolds. (English) Zbl 1158.65320 IMA J. Numer. Anal. 28, No. 4, 665-689 (2008). Reviewer: Aymée Marrero Severo (Habana) MSC: 65K05 90C48 90C51 PDF BibTeX XML Cite \textit{C. G. Baker} et al., IMA J. Numer. Anal. 28, No. 4, 665--689 (2008; Zbl 1158.65320) Full Text: DOI
Wang, Yunjuan; Zhu, Detong An affine scaling interior trust region method via optimal path for solving monotone variational inequality problem with linear constraints. (English) Zbl 1151.49025 Chin. Ann. Math., Ser. B 29, No. 3, 273-290 (2008). MSC: 49M15 90C33 PDF BibTeX XML Cite \textit{Y. Wang} and \textit{D. Zhu}, Chin. Ann. Math., Ser. B 29, No. 3, 273--290 (2008; Zbl 1151.49025) Full Text: DOI
Wang, JianYu; Ni, Qin An algorithm for solving new trust region subproblem with conic model. (English) Zbl 1148.49016 Sci. China, Ser. A 51, No. 3, 461-473 (2008). MSC: 49K10 90C30 49M29 PDF BibTeX XML Cite \textit{J. Wang} and \textit{Q. Ni}, Sci. China, Ser. A 51, No. 3, 461--473 (2008; Zbl 1148.49016) Full Text: DOI
Heinkenschloss, Matthias; Ridzal, Denis Integration of sequential quadratic programming and domain decomposition methods for nonlinear optimal control problems. (English) Zbl 1140.65333 Langer, Ulrich (ed.) et al., Domain decomposition methods in science and engineering XVII. Selected papers based on the presentations at the 17th international conference on domain decomposition methods, St. Wolfgang/Strobl, Austria, July 3–7, 2006. Berlin: Springer (ISBN 978-3-540-75198-4/pbk). Lecture Notes in Computational Science and Engineering 60, 69-80 (2008). MSC: 65K10 49J20 49M27 49M37 PDF BibTeX XML Cite \textit{M. Heinkenschloss} and \textit{D. Ridzal}, Lect. Notes Comput. Sci. Eng. 60, 69--80 (2008; Zbl 1140.65333) Full Text: DOI
Zhang, Xiaowei; Liu, Sanyang Genetic algorithm based on trust region method. (Chinese. English summary) Zbl 1174.65426 Syst. Eng. Electron. 29, No. 8, 1377-1380, 1384 (2007). MSC: 65K05 90C59 90C51 90C15 PDF BibTeX XML Cite \textit{X. Zhang} and \textit{S. Liu}, Syst. Eng. Electron. 29, No. 8, 1377--1380, 1384 (2007; Zbl 1174.65426)
Yang, Chao; Meza, Juan C.; Wang, Lin-Wang A trust region direct constrained minimization algorithm for the Kohn-Sham equation. (English) Zbl 1154.65340 SIAM J. Sci. Comput. 29, No. 5, 1854-1875 (2007). MSC: 65K10 PDF BibTeX XML Cite \textit{C. Yang} et al., SIAM J. Sci. Comput. 29, No. 5, 1854--1875 (2007; Zbl 1154.65340) Full Text: DOI DOI
Li, Gaidi; Wang, Yanfei A regularizing trust region algorithm for nonlinear ill-posed problems. (English) Zbl 1200.65041 Inverse Probl. Sci. Eng. 14, No. 8, 859-872 (2006). MSC: 65J20 65J22 65J15 PDF BibTeX XML Cite \textit{G. Li} and \textit{Y. Wang}, Inverse Probl. Sci. Eng. 14, No. 8, 859--872 (2006; Zbl 1200.65041) Full Text: DOI
Ma, Changfeng A smooth trust region algorithm for the nonlinear complementarity problems. (Chinese. English summary) Zbl 1121.90411 Chin. J. Eng. Math. 23, No. 1, 20-28 (2006). MSC: 90C33 PDF BibTeX XML Cite \textit{C. Ma}, Chin. J. Eng. Math. 23, No. 1, 20--28 (2006; Zbl 1121.90411)
Nie, Pu-yan CDT like approaches for the system of nonlinear equations. (English) Zbl 1088.65049 Appl. Math. Comput. 172, No. 2, 892-902 (2006). MSC: 65H10 65K05 90C30 PDF BibTeX XML Cite \textit{P.-y. Nie}, Appl. Math. Comput. 172, No. 2, 892--902 (2006; Zbl 1088.65049) Full Text: DOI
Absil, P.-A.; Baker, C. G.; Gallivan, K. A. A truncated-CG style method for symmetric generalized eigenvalue problems. (English) Zbl 1090.65042 J. Comput. Appl. Math. 189, No. 1-2, 274-285 (2006). Reviewer: Amin Boumenir (Carrollton) MSC: 65F15 PDF BibTeX XML Cite \textit{P. A. Absil} et al., J. Comput. Appl. Math. 189, No. 1--2, 274--285 (2006; Zbl 1090.65042) Full Text: DOI
Bakushinsky, A. B.; Khan, T.; Smirnova, A. Inverse problem in optical tomography and its numerical investigation by iteratively regularized methods. (English) Zbl 1090.65146 J. Inverse Ill-Posed Probl. 13, No. 3-6, 57-551 (2005). MSC: 65R20 45K05 45Q05 92C55 PDF BibTeX XML Cite \textit{A. B. Bakushinsky} et al., J. Inverse Ill-Posed Probl. 13, No. 3--6, 57--551 (2005; Zbl 1090.65146) Full Text: DOI
Yamashita, Hiroshi; Dan, Hiroshige Global convergence of trust region sequential quadratic programming method. (English) Zbl 1096.90038 J. Oper. Res. Soc. Japan 48, No. 1, 41-56 (2005). MSC: 90C30 90C55 PDF BibTeX XML Cite \textit{H. Yamashita} and \textit{H. Dan}, J. Oper. Res. Soc. Japan 48, No. 1, 41--56 (2005; Zbl 1096.90038) Full Text: DOI
Walmag, Jérôme M. B.; Delhez, Éric J. M. A trust-region method applied to parameter identification of a simple prey-predator model. (English) Zbl 1077.65083 Appl. Math. Modelling 29, No. 3, 289-307 (2005). MSC: 65L09 34A55 34A34 90C53 65K05 92D25 PDF BibTeX XML Cite \textit{J. M. B. Walmag} and \textit{É. J. M. Delhez}, Appl. Math. Modelling 29, No. 3, 289--307 (2005; Zbl 1077.65083) Full Text: DOI
Ho, H. W.; Wong, S. C. A Levenberg-Marquardt iterative solver for least-squares problems. (English) Zbl 1071.65044 Commun. Numer. Methods Eng. 21, No. 6, 327-335 (2005). MSC: 65F20 PDF BibTeX XML Cite \textit{H. W. Ho} and \textit{S. C. Wong}, Commun. Numer. Methods Eng. 21, No. 6, 327--335 (2005; Zbl 1071.65044) Full Text: DOI
Chen, Huafu; Niu, Hai A feasible trust algorithm of nonlinear max-min problems. (Chinese. English summary) Zbl 1152.90654 J. Univ. Electron. Sci. Technol. China 33, No. 4, 468-470 (2004). MSC: 90C47 PDF BibTeX XML Cite \textit{H. Chen} and \textit{H. Niu}, J. Univ. Electron. Sci. Technol. China 33, No. 4, 468--470 (2004; Zbl 1152.90654)
Yu, Zhensheng The bounded smooth reformulation and a trust region algorithm for semidefinite complementarity problems. (English) Zbl 1068.65083 Appl. Math. Comput. 159, No. 1, 157-170 (2004). Reviewer: Akrur Behera (Rourkela) MSC: 65K05 90C33 PDF BibTeX XML Cite \textit{Z. Yu}, Appl. Math. Comput. 159, No. 1, 157--170 (2004; Zbl 1068.65083) Full Text: DOI
Li, Chunfa; Feng, Enmin Optimality condition for infinite-dimensional programming problem with operator and bound constraints. (English) Zbl 1050.49019 J. Math. Res. Expo. 24, No. 2, 257-266 (2004). MSC: 49K27 90C48 49M37 90C51 90C55 PDF BibTeX XML Cite \textit{C. Li} and \textit{E. Feng}, J. Math. Res. Expo. 24, No. 2, 257--266 (2004; Zbl 1050.49019)
Calvetti, Daniela; Reichel, Lothar Gauss quadrature applied to trust region computations. (English) Zbl 1033.65039 Numer. Algorithms 34, No. 1, 85-102 (2003). Reviewer: Hans Benker (Merseburg) MSC: 65K05 90C06 90C60 90C53 PDF BibTeX XML Cite \textit{D. Calvetti} and \textit{L. Reichel}, Numer. Algorithms 34, No. 1, 85--102 (2003; Zbl 1033.65039) Full Text: DOI
Rojas, Marielba; Steihaug, Trond An interior-point trust-region-based method for large-scale non-negative regularization. (English) Zbl 1015.90062 Inverse Probl. 18, No. 5, 1291-1307 (2002). MSC: 90C20 65K05 PDF BibTeX XML Cite \textit{M. Rojas} and \textit{T. Steihaug}, Inverse Probl. 18, No. 5, 1291--1307 (2002; Zbl 1015.90062) Full Text: DOI
Gilles, Luc; Vogel, C.; Bardsley, J. Computational methods for a large-scale inverse problem arising in atmospheric optics. (English) Zbl 1005.78005 Inverse Probl. 18, No. 1, 237-252 (2002). MSC: 78A46 65R32 78M25 86A10 86A22 PDF BibTeX XML Cite \textit{L. Gilles} et al., Inverse Probl. 18, No. 1, 237--252 (2002; Zbl 1005.78005) Full Text: DOI