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
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
Xu, Peng; Roosta, Fred; Mahoney, Michael W. Newton-type methods for non-convex optimization under inexact Hessian information. (English) Zbl 1451.90134 Math. Program. 184, No. 1-2 (A), 35-70 (2020). MSC: 90C26 90C53 65K05 90C06 PDFBibTeX XMLCite \textit{P. Xu} et al., Math. Program. 184, No. 1--2 (A), 35--70 (2020; Zbl 1451.90134) 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
Xia, Yong; Wang, Longfei; Yang, Meijia A fast algorithm for globally solving Tikhonov regularized total least squares problem. (English) Zbl 1411.65065 J. Glob. Optim. 73, No. 2, 311-330 (2019). MSC: 65F20 90C26 90C32 90C20 PDFBibTeX XMLCite \textit{Y. Xia} et al., J. Glob. Optim. 73, No. 2, 311--330 (2019; Zbl 1411.65065) Full Text: DOI arXiv
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
Pospíšil, Lukáš; Dostál, Zdeněk The projected Barzilai-Borwein method with fall-back for strictly convex QCQP problems with separable constraints. (English) Zbl 1482.90135 Math. Comput. Simul. 145, 79-89 (2018). MSC: 90C20 90C30 90C53 65K05 74M15 PDFBibTeX XMLCite \textit{L. Pospíšil} and \textit{Z. Dostál}, Math. Comput. Simul. 145, 79--89 (2018; Zbl 1482.90135) 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
Beck, Amir; Vaisbourd, Yakov Globally solving the trust region subproblem using simple first-order methods. (English) Zbl 1455.90104 SIAM J. Optim. 28, No. 3, 1951-1967 (2018). Reviewer: Nicolae Popovici (Cluj-Napoca) MSC: 90C06 90C26 90C46 PDFBibTeX XMLCite \textit{A. Beck} and \textit{Y. Vaisbourd}, SIAM J. Optim. 28, No. 3, 1951--1967 (2018; Zbl 1455.90104) 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
Gao, Guohua; Vink, Jeroen C.; Chen, Chaohui; El Khamra, Yaakoub; Tarrahi, Mohammadali Distributed Gauss-Newton optimization method for history matching problems with multiple best matches. (English) Zbl 1405.90126 Comput. Geosci. 21, No. 5-6, 1325-1342 (2017). MSC: 90C30 90C55 90C56 PDFBibTeX XMLCite \textit{G. Gao} et al., Comput. Geosci. 21, No. 5--6, 1325--1342 (2017; Zbl 1405.90126) 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
Ho-Nguyen, Nam; Kilinç-Karzan, Fatma A second-order cone based approach for solving the trust-region subproblem and its variants. (English) Zbl 1370.90170 SIAM J. Optim. 27, No. 3, 1485-1512 (2017). MSC: 90C20 90C25 90C26 90C30 PDFBibTeX XMLCite \textit{N. Ho-Nguyen} and \textit{F. Kilinç-Karzan}, SIAM J. Optim. 27, No. 3, 1485--1512 (2017; Zbl 1370.90170) 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
Hazan, Elad; Koren, Tomer A linear-time algorithm for trust region problems. (English) Zbl 1346.90654 Math. Program. 158, No. 1-2 (A), 363-381 (2016). MSC: 90C20 90C22 90C26 68W25 PDFBibTeX XMLCite \textit{E. Hazan} and \textit{T. Koren}, Math. Program. 158, No. 1--2 (A), 363--381 (2016; Zbl 1346.90654) Full Text: DOI arXiv
Chen, Yi; Gao, David Yang Canonical dual approach for minimizing a nonconvex quadratic function over a sphere. (English) Zbl 1327.90164 Gao, David (ed.) et al., Advances in global optimization. Selected papers based on the presentations at the 3rd world congress on global optimization in engineering and science, WCGO, Anhui, China, July 8–12, 2013. Cham: Springer (ISBN 978-3-319-08376-6/hbk; 978-3-319-08377-3/ebook). Springer Proceedings in Mathematics & Statistics 95, 149-156 (2015). MSC: 90C20 90C26 90C46 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{D. Y. Gao}, Springer Proc. Math. Stat. 95, 149--156 (2015; Zbl 1327.90164) Full Text: DOI
Bouchala, Jiří; Dostál, Zdeněk; Kozubek, Tomáš; Pospíšil, Lukáš; Vodstrčil, Petr On the solution of convex QPQC problems with elliptic and other separable constraints with strong curvature. (English) Zbl 1338.90290 Appl. Math. Comput. 247, 848-864 (2014). MSC: 90C20 90C25 PDFBibTeX XMLCite \textit{J. Bouchala} et al., Appl. Math. Comput. 247, 848--864 (2014; Zbl 1338.90290) 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
Fyodorov, Yan V.; Le Doussal, Pierre Topology trivialization and large deviations for the minimum in the simplest random optimization. (English) Zbl 1291.82127 J. Stat. Phys. 154, No. 1-2, 466-490 (2014). MSC: 82D30 49N10 60F10 60B20 15B52 PDFBibTeX XMLCite \textit{Y. V. Fyodorov} and \textit{P. Le Doussal}, J. Stat. Phys. 154, No. 1--2, 466--490 (2014; Zbl 1291.82127) Full Text: DOI arXiv
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
Bouchala, J.; Dostál, Z.; Vodstrčil, P. Separable spherical constraints and the decrease of a quadratic function in the gradient projection step. (English) Zbl 1266.90137 J. Optim. Theory Appl. 157, No. 1, 132-140 (2013). MSC: 90C20 90C25 PDFBibTeX XMLCite \textit{J. Bouchala} et al., J. Optim. Theory Appl. 157, No. 1, 132--140 (2013; Zbl 1266.90137) Full Text: DOI
Dostál, Zdeněk; Kozubek, Tomáš An optimal algorithm and superrelaxation for minimization of a quadratic function subject to separable convex constraints with applications. (English) Zbl 1259.65089 Math. Program. 135, No. 1-2 (A), 195-220 (2012). Reviewer: Hans Benker (Merseburg) MSC: 65K05 90C20 90C90 PDFBibTeX XMLCite \textit{Z. Dostál} and \textit{T. Kozubek}, Math. Program. 135, No. 1--2 (A), 195--220 (2012; Zbl 1259.65089) 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
Apostolopoulou, M. S.; Sotiropoulos, D. G.; Botsaris, C. A.; Pintelas, P. A practical method for solving large-scale TRS. (English) Zbl 1220.90077 Optim. Lett. 5, No. 2, 207-227 (2011). MSC: 90C20 90C06 PDFBibTeX XMLCite \textit{M. S. Apostolopoulou} et al., Optim. Lett. 5, No. 2, 207--227 (2011; Zbl 1220.90077) Full Text: DOI
Salahi, Maziar Convex optimization approach to a single quadratically constrained quadratic minimization problem. (English) Zbl 1204.90075 CEJOR, Cent. Eur. J. Oper. Res. 18, No. 2, 181-187 (2010). MSC: 90C25 90C20 PDFBibTeX XMLCite \textit{M. Salahi}, CEJOR, Cent. Eur. J. Oper. Res. 18, No. 2, 181--187 (2010; Zbl 1204.90075) Full Text: DOI
Beck, Amir; Teboulle, Marc A convex optimization approach for minimizing the ratio of indefinite quadratic functions over an ellipsoid. (English) Zbl 1176.90451 Math. Program. 118, No. 1 (A), 13-35 (2009). Reviewer: Jean-Jacques Strodiot (Namur) MSC: 90C22 90C25 62G05 PDFBibTeX XMLCite \textit{A. Beck} and \textit{M. Teboulle}, Math. Program. 118, No. 1 (A), 13--35 (2009; Zbl 1176.90451) Full Text: DOI
Grodzevich, Oleg; Wolkowicz, Henry Regularization using a parameterized trust region subproblem. (English) Zbl 1165.90023 Math. Program. 116, No. 1-2 (B), 193-220 (2009). MSC: 90C30 PDFBibTeX XMLCite \textit{O. Grodzevich} and \textit{H. Wolkowicz}, Math. Program. 116, No. 1--2 (B), 193--220 (2009; Zbl 1165.90023) Full Text: DOI
Sun, Wenyu; Hou, Liusheng; Dang, Chuangying A modified trust region method with beale’s PCG technique for optimization. (English) Zbl 1146.90074 Comput. Optim. Appl. 40, No. 1, 59-72 (2008). MSC: 90C30 90C52 PDFBibTeX XMLCite \textit{W. Sun} et al., Comput. Optim. Appl. 40, No. 1, 59--72 (2008; Zbl 1146.90074) 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
Hager, William W.; Park, Soonchul Global convergence of SSM for minimizing a quadratic over a sphere. (English) Zbl 1059.90112 Math. Comput. 74, No. 251, 1413-1423 (2005). MSC: 90C20 65F10 65Y20 PDFBibTeX XMLCite \textit{W. W. Hager} and \textit{S. Park}, Math. Comput. 74, No. 251, 1413--1423 (2005; Zbl 1059.90112) Full Text: DOI
Yin, Hongxia; Han, Jiye; Chen, Zhongwen Global convergence of a trust region algorithm for nonlinear inequality constrained optimization problems. (English) Zbl 1070.65044 Numer. Funct. Anal. Optimization 25, No. 5-6, 571-592 (2004). Reviewer: Nada Djuranović-Miličić (Belgrade) MSC: 65K05 90C30 90C55 PDFBibTeX XMLCite \textit{H. Yin} et al., Numer. Funct. Anal. Optim. 25, No. 5--6, 571--592 (2004; Zbl 1070.65044) Full Text: DOI
Fortin, Charles; Wolkowicz, Henry The trust region subproblem and semidefinite programming. (English) Zbl 1070.65041 Optim. Methods Softw. 19, No. 1, 41-67 (2004). Reviewer: Klaus Schittkowski (Bayreuth) MSC: 65K05 90C22 90C20 90C30 90C06 90C55 PDFBibTeX XMLCite \textit{C. Fortin} and \textit{H. Wolkowicz}, Optim. Methods Softw. 19, No. 1, 41--67 (2004; Zbl 1070.65041) Full Text: DOI
Abdel-Aziz, Mohammedi R. Implicitly restarted projection algorithm for solving optimization problems. (English) Zbl 0965.65089 Numer. Funct. Anal. Optimization 21, No. 3-4, 319-336 (2000). Reviewer: N.Djuranović-Miličić (Beograd) MSC: 65K05 90C20 PDFBibTeX XMLCite \textit{M. R. Abdel-Aziz}, Numer. Funct. Anal. Optim. 21, No. 3--4, 319--336 (2000; Zbl 0965.65089) Full Text: DOI
Sadjadi, Seyed Jafar; Ponnambalam, K. Advances in trust region algorithms for constrained optimization. (English) Zbl 0956.90048 Appl. Numer. Math. 29, No. 3, 423-443 (1999). MSC: 90C30 49M37 49M30 PDFBibTeX XMLCite \textit{S. J. Sadjadi} and \textit{K. Ponnambalam}, Appl. Numer. Math. 29, No. 3, 423--443 (1999; Zbl 0956.90048) Full Text: DOI