Gao, Guohua; Wang, Yixuan; Vink, Jeroen C.; Wells, Terence J.; Saaf, Fredrik J. F. E. Distributed quasi-Newton derivative-free optimization method for optimization problems with multiple local optima. (English) Zbl 1496.65069 Comput. Geosci. 26, No. 4, 847-863 (2022). MSC: 65K05 86A05 90C39 86A32 65K10 PDFBibTeX XMLCite \textit{G. Gao} et al., Comput. Geosci. 26, No. 4, 847--863 (2022; Zbl 1496.65069) Full Text: DOI
Jia, Xiaojing; Liang, Xin; Shen, Chungen; Zhang, Lei-Hong Solving the cubic regularization model by a nested restarting Lanczos method. (English) Zbl 1489.90183 SIAM J. Matrix Anal. Appl. 43, No. 2, 812-839 (2022). MSC: 90C30 90C06 90C53 65K05 65F15 PDFBibTeX XMLCite \textit{X. Jia} et al., SIAM J. Matrix Anal. Appl. 43, No. 2, 812--839 (2022; Zbl 1489.90183) Full Text: DOI
Zeng, Liaoyuan; Pong, Ting Kei \(\rho\)-regularization subproblems: strong duality and an eigensolver-based algorithm. (English) Zbl 1487.90609 Comput. Optim. Appl. 81, No. 2, 337-368 (2022). MSC: 90C30 90C46 PDFBibTeX XMLCite \textit{L. Zeng} and \textit{T. K. Pong}, Comput. Optim. Appl. 81, No. 2, 337--368 (2022; Zbl 1487.90609) Full Text: DOI arXiv
Lampe, Jörg; Voss, Heinrich A survey on variational characterizations for nonlinear eigenvalue problems. (English) Zbl 07436835 ETNA, Electron. Trans. Numer. Anal. 55, 1-75 (2022). MSC: 65-XX 35P30 47A52 47A75 47J10 65F15 PDFBibTeX XMLCite \textit{J. Lampe} and \textit{H. Voss}, ETNA, Electron. Trans. Numer. Anal. 55, 1--75 (2022; Zbl 07436835) Full Text: DOI Link
Jia, Zhongxiao; Wang, Fa The convergence of the generalized Lanczos trust-region method for the trust-region subproblem. (English) Zbl 1462.90083 SIAM J. Optim. 31, No. 1, 887-914 (2021). MSC: 90C20 90C30 65K05 65F10 PDFBibTeX XMLCite \textit{Z. Jia} and \textit{F. Wang}, SIAM J. Optim. 31, No. 1, 887--914 (2021; Zbl 1462.90083) Full Text: DOI arXiv
Erway, Jennifer B.; Griffin, Joshua; Marcia, Roummel F.; Omheni, Riadh Trust-region algorithms for training responses: machine learning methods using indefinite Hessian approximations. (English) Zbl 1440.90092 Optim. Methods Softw. 35, No. 3, 460-487 (2020). MSC: 90C53 15A06 90C06 65K05 65K10 49M15 PDFBibTeX XMLCite \textit{J. B. Erway} et al., Optim. Methods Softw. 35, No. 3, 460--487 (2020; Zbl 1440.90092) Full Text: DOI arXiv
Gao, Guohua; Jiang, Hao; Vink, Jeroen C.; van Hagen, Paul P. H.; Wells, Terence J. Performance enhancement of Gauss-Newton trust-region solver for distributed Gauss-Newton optimization method. (English) Zbl 1434.90211 Comput. Geosci. 24, No. 2, 837-852 (2020). MSC: 90C39 90C20 86A22 90C55 PDFBibTeX XMLCite \textit{G. Gao} et al., Comput. Geosci. 24, No. 2, 837--852 (2020; Zbl 1434.90211) Full Text: DOI
Gould, Nicholas I. M.; Simoncini, Valeria Error estimates for iterative algorithms for minimizing regularized quadratic subproblems. (English) Zbl 1428.90160 Optim. Methods Softw. 35, No. 2, 304-328 (2020). MSC: 90C30 65K05 90C20 PDFBibTeX XMLCite \textit{N. I. M. Gould} and \textit{V. Simoncini}, Optim. Methods Softw. 35, No. 2, 304--328 (2020; Zbl 1428.90160) Full Text: DOI Link
Adachi, Satoru; Nakatsukasa, Yuji Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint. (English) Zbl 1411.90246 Math. Program. 173, No. 1-2 (A), 79-116 (2019). MSC: 90C20 90C30 65K05 PDFBibTeX XMLCite \textit{S. Adachi} and \textit{Y. Nakatsukasa}, Math. Program. 173, No. 1--2 (A), 79--116 (2019; Zbl 1411.90246) Full Text: DOI
Kolvenbach, Philip; Lass, Oliver; Ulbrich, Stefan An approach for robust PDE-constrained optimization with application to shape optimization of electrical engines and of dynamic elastic structures under uncertainty. (English) Zbl 1507.49020 Optim. Eng. 19, No. 3, 697-731 (2018). MSC: 49K20 35Q74 49K35 74P20 PDFBibTeX XMLCite \textit{P. Kolvenbach} et al., Optim. Eng. 19, No. 3, 697--731 (2018; Zbl 1507.49020) Full Text: DOI
Zhang, Leihong; Yang, Weihong; Shen, Chungen; Feng, Jiang Error bounds of Lanczos approach for trust-region subproblem. (English) Zbl 1392.90088 Front. Math. China 13, No. 2, 459-481 (2018). MSC: 90C20 90C06 65F10 65F15 65F35 PDFBibTeX XMLCite \textit{L. Zhang} et al., Front. Math. China 13, No. 2, 459--481 (2018; Zbl 1392.90088) Full Text: DOI
Zhang, Lei-Hong; Shen, Chungen A nested Lanczos method for the trust-region subproblem. (English) Zbl 1402.90113 SIAM J. Sci. Comput. 40, No. 4, A2005-A2032 (2018). MSC: 90C20 90C06 65F10 65F15 65K05 PDFBibTeX XMLCite \textit{L.-H. Zhang} and \textit{C. Shen}, SIAM J. Sci. Comput. 40, No. 4, A2005--A2032 (2018; Zbl 1402.90113) Full Text: DOI
Lenders, Felix; Kirches, C.; Potschka, A. trlib: a vector-free implementation of the GLTR method for iterative solution of the trust region problem. (English) Zbl 1390.35364 Optim. Methods Softw. 33, No. 3, 420-449 (2018). MSC: 35Q90 65K05 90C20 90C30 PDFBibTeX XMLCite \textit{F. Lenders} et al., Optim. Methods Softw. 33, No. 3, 420--449 (2018; Zbl 1390.35364) Full Text: DOI arXiv
Zhang, Lei-Hong; Shen, Chungen; Yang, Wei Hong; Júdice, Joaquim J. A Lanczos method for large-scale extreme Lorentz eigenvalue problems. (English) Zbl 1390.90543 SIAM J. Matrix Anal. Appl. 39, No. 2, 611-631 (2018). MSC: 90C33 47J20 15A18 90C06 65F15 PDFBibTeX XMLCite \textit{L.-H. Zhang} et al., SIAM J. Matrix Anal. Appl. 39, No. 2, 611--631 (2018; Zbl 1390.90543) Full Text: DOI
Zhang, Lei-Hong; Shen, Chungen; Li, Ren-Cang On the generalized Lanczos trust-region method. (English) Zbl 1380.90210 SIAM J. Optim. 27, No. 3, 2110-2142 (2017). MSC: 90C20 90C06 65F10 65F15 65F35 PDFBibTeX XMLCite \textit{L.-H. Zhang} et al., SIAM J. Optim. 27, No. 3, 2110--2142 (2017; Zbl 1380.90210) Full Text: DOI
Birgin, E. G.; Martínez, J. M. The use of quadratic regularization with a cubic descent condition for unconstrained optimization. (English) Zbl 1370.90260 SIAM J. Optim. 27, No. 2, 1049-1074 (2017). MSC: 90C30 65K05 49M37 90C60 68Q25 PDFBibTeX XMLCite \textit{E. G. Birgin} and \textit{J. M. Martínez}, SIAM J. Optim. 27, No. 2, 1049--1074 (2017; Zbl 1370.90260) Full Text: DOI
Brust, Johannes; Erway, Jennifer B.; Marcia, Roummel F. On solving L-SR1 trust-region subproblems. (English) Zbl 1364.90239 Comput. Optim. Appl. 66, No. 2, 245-266 (2017). MSC: 90C20 65K05 PDFBibTeX XMLCite \textit{J. Brust} et al., Comput. Optim. Appl. 66, No. 2, 245--266 (2017; Zbl 1364.90239) 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 PDFBibTeX XMLCite \textit{S. Adachi} et al., SIAM J. Optim. 27, No. 1, 269--291 (2017; Zbl 1359.49009) Full Text: DOI
Zhang, Lei-Hong; Yang, Wei Hong; Shen, Chungen; Li, Ren-Cang A Krylov subspace method for large-scale second-order cone linear complementarity problem. (English) Zbl 1326.90090 SIAM J. Sci. Comput. 37, No. 4, A2046-A2075 (2015). MSC: 90C33 65K05 65F99 65F15 65F30 65P99 PDFBibTeX XMLCite \textit{L.-H. Zhang} et al., SIAM J. Sci. Comput. 37, No. 4, A2046--A2075 (2015; Zbl 1326.90090) Full Text: DOI Link
Behboodi-Kahoo, Malihe; Ketabchi, Saeed Parametric approach for correcting inconsistent linear equality system. (English) Zbl 1298.90102 Optim. Methods Softw. 29, No. 6, 1317-1322 (2014). MSC: 90C30 90C31 15A39 PDFBibTeX XMLCite \textit{M. Behboodi-Kahoo} and \textit{S. Ketabchi}, Optim. Methods Softw. 29, No. 6, 1317--1322 (2014; Zbl 1298.90102) Full Text: DOI
Pong, Ting Kei; Wolkowicz, Henry The generalized trust region subproblem. (English) Zbl 1329.90100 Comput. Optim. Appl. 58, No. 2, 273-322 (2014). MSC: 90C20 PDFBibTeX XMLCite \textit{T. K. Pong} and \textit{H. Wolkowicz}, Comput. Optim. Appl. 58, No. 2, 273--322 (2014; Zbl 1329.90100) Full Text: DOI
Rojas, Marielba; Fotland, Bjørn H.; Steihaug, Trond Computational and sensitivity aspects of eigenvalue-based methods for the large-scale trust-region subproblem. (English) Zbl 1273.90142 Optim. Methods Softw. 28, No. 3, 564-580 (2013). MSC: 90C20 90C06 90C51 PDFBibTeX XMLCite \textit{M. Rojas} et al., Optim. Methods Softw. 28, No. 3, 564--580 (2013; Zbl 1273.90142) Full Text: DOI Link
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 PDFBibTeX XMLCite \textit{D. R. Martin} and \textit{L. Reichel}, BIT 53, No. 1, 153--173 (2013; Zbl 1262.65053) Full Text: DOI
Gratton, Serge; Gürol, Selime; Toint, Philippe L. Preconditioning and globalizing conjugate gradients in dual space for quadratically penalized nonlinear-least squares problems. (English) Zbl 1267.90093 Comput. Optim. Appl. 54, No. 1, 1-25 (2013). MSC: 90C20 90C52 PDFBibTeX XMLCite \textit{S. Gratton} et al., Comput. Optim. Appl. 54, No. 1, 1--25 (2013; Zbl 1267.90093) Full Text: DOI
Landi, G.; Loli Piccolomini, E. A feasible direction method for image restoration. (English) Zbl 1261.90055 Optim. Lett. 6, No. 8, 1795-1817 (2012). MSC: 90C30 90C90 PDFBibTeX XMLCite \textit{G. Landi} and \textit{E. Loli Piccolomini}, Optim. Lett. 6, No. 8, 1795--1817 (2012; Zbl 1261.90055) Full Text: DOI
Benner, Peter; Embree, Mark; Lehoucq, Richard B.; Kelley, C. T. A mathematical biography of Danny C. Sorensen. (English) Zbl 1238.01104 Linear Algebra Appl. 436, No. 8, 2717-2724 (2012). MSC: 01A70 PDFBibTeX XMLCite \textit{P. Benner} et al., Linear Algebra Appl. 436, No. 8, 2717--2724 (2012; Zbl 1238.01104) Full Text: DOI
Li, Qingna; Qi, Houduo; Xiu, Naihua Block relaxation and majorization methods for the nearest correlation matrix with factor structure. (English) Zbl 1236.90119 Comput. Optim. Appl. 50, No. 2, 327-349 (2011). MSC: 90C30 65K05 PDFBibTeX XMLCite \textit{Q. Li} et al., Comput. Optim. Appl. 50, No. 2, 327--349 (2011; Zbl 1236.90119) Full Text: DOI
Loli Piccolomini, E.; Zama, F. An iterative algorithm for large size least-squares constrained regularization problems. (English) Zbl 1228.65061 Appl. Math. Comput. 217, No. 24, 10343-10354 (2011). Reviewer: Tzvetan Semerdjiev (Sofia) MSC: 65F22 65F20 65K05 65Y20 PDFBibTeX XMLCite \textit{E. Loli Piccolomini} and \textit{F. Zama}, Appl. Math. Comput. 217, No. 24, 10343--10354 (2011; Zbl 1228.65061) Full Text: DOI
Kearsley, Anthony J. Matrix-free algorithm for the large-scale constrained trust-region subproblem. (English) Zbl 1095.90086 Optim. Methods Softw. 21, No. 2, 233-245 (2006). MSC: 90C20 65K10 PDFBibTeX XMLCite \textit{A. J. Kearsley}, Optim. Methods Softw. 21, No. 2, 233--245 (2006; Zbl 1095.90086) Full Text: DOI
Eldén, L.; Hansen, P. C.; Rojas, M. Minimization of linear functionals defined on solutions of large-scale discrete ill-posed problems. (English) Zbl 1084.65035 BIT 45, No. 2, 329-340 (2005). Reviewer: R. P. Tewarson (Stony Brook) MSC: 65F22 65F20 PDFBibTeX XMLCite \textit{L. Eldén} et al., BIT 45, No. 2, 329--340 (2005; Zbl 1084.65035) Full Text: DOI