Song, Mengmeng; Xia, Yong Linear programming on the Stiefel manifold. (English) Zbl 07809689 SIAM J. Optim. 34, No. 1, 718-741 (2024). MSC: 90C26 90C22 90C46 90C20 PDFBibTeX XMLCite \textit{M. Song} and \textit{Y. Xia}, SIAM J. Optim. 34, No. 1, 718--741 (2024; Zbl 07809689) Full Text: DOI arXiv
Bertsimas, Dimitris; Cory-Wright, Ryan; Pauphilet, Jean A new perspective on low-rank optimization. (English) Zbl 1522.90075 Math. Program. 202, No. 1-2 (A), 47-92 (2023); correction ibid. 202, No. 1-2 (A), 93-94 (2023). MSC: 90C22 90C25 90C26 15A03 26B25 PDFBibTeX XMLCite \textit{D. Bertsimas} et al., Math. Program. 202, No. 1--2 (A), 47--92 (2023; Zbl 1522.90075) Full Text: DOI arXiv OA License
Legat, Benoît; Yuan, Chenyang; Parrilo, Pablo Low-rank univariate sum of squares has no spurious local minima. (English) Zbl 1522.90082 SIAM J. Optim. 33, No. 3, 2041-2061 (2023). MSC: 90C23 90C26 90C22 PDFBibTeX XMLCite \textit{B. Legat} et al., SIAM J. Optim. 33, No. 3, 2041--2061 (2023; Zbl 1522.90082) Full Text: DOI arXiv
He, Chuan; Lu, Zhaosong; Pong, Ting Kei A Newton-CG based augmented Lagrangian method for finding a second-order stationary point of nonconvex equality constrained optimization with complexity guarantees. (English) Zbl 1522.65092 SIAM J. Optim. 33, No. 3, 1734-1766 (2023). MSC: 65K05 90C26 68Q25 90C06 90C30 90C60 PDFBibTeX XMLCite \textit{C. He} et al., SIAM J. Optim. 33, No. 3, 1734--1766 (2023; Zbl 1522.65092) Full Text: DOI arXiv
Wang, Yifei; Deng, Kangkang; Liu, Haoyang; Wen, Zaiwen A decomposition augmented Lagrangian method for low-rank semidefinite programming. (English) Zbl 1522.90032 SIAM J. Optim. 33, No. 3, 1361-1390 (2023). MSC: 90C06 90C22 90C26 90C56 PDFBibTeX XMLCite \textit{Y. Wang} et al., SIAM J. Optim. 33, No. 3, 1361--1390 (2023; Zbl 1522.90032) Full Text: DOI arXiv
Ling, Shuyang Solving orthogonal group synchronization via convex and low-rank optimization: tightness and landscape analysis. (English) Zbl 1519.90156 Math. Program. 200, No. 1 (A), 589-628 (2023). MSC: 90C22 90C26 90C46 62F10 PDFBibTeX XMLCite \textit{S. Ling}, Math. Program. 200, No. 1 (A), 589--628 (2023; Zbl 1519.90156) Full Text: DOI arXiv
Qian, Yitian; Pan, Shaohua; Bi, Shujun A matrix nonconvex relaxation approach to unconstrained binary polynomial programs. (English) Zbl 1516.90045 Comput. Optim. Appl. 84, No. 3, 875-919 (2023). MSC: 90C23 90C27 90C22 90C26 PDFBibTeX XMLCite \textit{Y. Qian} et al., Comput. Optim. Appl. 84, No. 3, 875--919 (2023; Zbl 1516.90045) Full Text: DOI
Bertsimas, Dimitris; Cory-Wright, Ryan; Pauphilet, Jean Mixed-projection conic optimization: a new paradigm for modeling rank constraints. (English) Zbl 1510.90259 Oper. Res. 70, No. 6, 3321-3344 (2022). MSC: 90C30 90C22 90C26 90C10 90C59 PDFBibTeX XMLCite \textit{D. Bertsimas} et al., Oper. Res. 70, No. 6, 3321--3344 (2022; Zbl 1510.90259) Full Text: DOI arXiv
Erdogdu, Murat A.; Ozdaglar, Asuman; Parrilo, Pablo A.; Vanli, Nuri Denizcan Convergence rate of block-coordinate maximization Burer-Monteiro method for solving large SDPs. (English) Zbl 1505.65213 Math. Program. 195, No. 1-2 (A), 243-281 (2022). MSC: 65K05 90C22 90C25 90C26 PDFBibTeX XMLCite \textit{M. A. Erdogdu} et al., Math. Program. 195, No. 1--2 (A), 243--281 (2022; Zbl 1505.65213) Full Text: DOI arXiv
Wang, Peng; Zhou, Zirui; So, Anthony Man-Cho Non-convex exact community recovery in stochastic block model. (English) Zbl 1505.05120 Math. Program. 195, No. 1-2 (A), 1-37 (2022). MSC: 05C82 90C10 05C90 90C26 62H25 62G20 91D30 PDFBibTeX XMLCite \textit{P. Wang} et al., Math. Program. 195, No. 1--2 (A), 1--37 (2022; Zbl 1505.05120) Full Text: DOI arXiv
Dey, Santanu S.; Kazachkov, Aleksandr; Lodi, Andrea; Munoz, Gonzalo Cutting plane generation through sparse principal component analysis. (English) Zbl 1494.90083 SIAM J. Optim. 32, No. 2, 1319-1343 (2022). MSC: 90C26 90C20 90-08 PDFBibTeX XMLCite \textit{S. S. Dey} et al., SIAM J. Optim. 32, No. 2, 1319--1343 (2022; Zbl 1494.90083) Full Text: DOI
Ling, Shuyang Improved performance guarantees for orthogonal group synchronization via generalized power method. (English) Zbl 1493.90145 SIAM J. Optim. 32, No. 2, 1018-1048 (2022). MSC: 90C26 90C30 90C46 PDFBibTeX XMLCite \textit{S. Ling}, SIAM J. Optim. 32, No. 2, 1018--1048 (2022; Zbl 1493.90145) Full Text: DOI arXiv
Wang, Alex L.; Kılınç-Karzan, Fatma On the tightness of SDP relaxations of QCQPs. (English) Zbl 1491.90114 Math. Program. 193, No. 1 (A), 33-73 (2022). MSC: 90C20 90C22 90C26 PDFBibTeX XMLCite \textit{A. L. Wang} and \textit{F. Kılınç-Karzan}, Math. Program. 193, No. 1 (A), 33--73 (2022; Zbl 1491.90114) Full Text: DOI arXiv
Li, Ji; Cai, Jian-Feng; Zhao, Hongkai Scalable incremental nonconvex optimization approach for phase retrieval. (English) Zbl 1466.90078 J. Sci. Comput. 87, No. 2, Paper No. 43, 26 p. (2021). MSC: 90C26 90C22 49N45 94A20 PDFBibTeX XMLCite \textit{J. Li} et al., J. Sci. Comput. 87, No. 2, Paper No. 43, 26 p. (2021; Zbl 1466.90078) Full Text: DOI arXiv
Hu, Jiang; Liu, Xin; Wen, Zai-Wen; Yuan, Ya-Xiang A brief introduction to manifold optimization. (English) Zbl 1474.49093 J. Oper. Res. Soc. China 8, No. 2, 199-248 (2020). MSC: 49Q99 65K05 90C22 90C26 90C27 90C30 PDFBibTeX XMLCite \textit{J. Hu} et al., J. Oper. Res. Soc. China 8, No. 2, 199--248 (2020; Zbl 1474.49093) Full Text: DOI arXiv
Chen, Yuxin; Chi, Yuejie; Fan, Jianqing; Ma, Cong; Yan, Yuling Noisy matrix completion: understanding statistical guarantees for convex relaxation via nonconvex optimization. (English) Zbl 1477.90060 SIAM J. Optim. 30, No. 4, 3098-3121 (2020). Reviewer: Sorin-Mihai Grad (Paris) MSC: 90C25 90C26 PDFBibTeX XMLCite \textit{Y. Chen} et al., SIAM J. Optim. 30, No. 4, 3098--3121 (2020; Zbl 1477.90060) Full Text: DOI arXiv
Ha, Wooseok; Liu, Haoyang; Barber, Rina Foygel An equivalence between critical points for rank constraints versus low-rank factorizations. (English) Zbl 1453.90127 SIAM J. Optim. 30, No. 4, 2927-2955 (2020). MSC: 90C26 PDFBibTeX XMLCite \textit{W. Ha} et al., SIAM J. Optim. 30, No. 4, 2927--2955 (2020; Zbl 1453.90127) Full Text: DOI arXiv
Carmon, Yair; Duchi, John C.; Hinder, Oliver; Sidford, Aaron Lower bounds for finding stationary points I. (English) Zbl 1451.90128 Math. Program. 184, No. 1-2 (A), 71-120 (2020). MSC: 90C26 90C06 90C60 68Q25 PDFBibTeX XMLCite \textit{Y. Carmon} et al., Math. Program. 184, No. 1--2 (A), 71--120 (2020; Zbl 1451.90128) Full Text: DOI arXiv
Waldspurger, Irène; Waters, Alden Rank optimality for the Burer-Monteiro factorization. (English) Zbl 1451.90114 SIAM J. Optim. 30, No. 3, 2577-2602 (2020). MSC: 90C22 90C26 65K10 PDFBibTeX XMLCite \textit{I. Waldspurger} and \textit{A. Waters}, SIAM J. Optim. 30, No. 3, 2577--2602 (2020; Zbl 1451.90114) Full Text: DOI arXiv
Burer, Samuel; Ye, Yinyu Exact semidefinite formulations for a class of (random and non-random) nonconvex quadratic programs. (English) Zbl 1445.90073 Math. Program. 181, No. 1 (A), 1-17 (2020); correction ibid. 190, No. 1-2 (A), 845-848 (2021). MSC: 90C20 90C22 90C26 PDFBibTeX XMLCite \textit{S. Burer} and \textit{Y. Ye}, Math. Program. 181, No. 1 (A), 1--17 (2020; Zbl 1445.90073) Full Text: DOI arXiv
Li, Xiao; Zhu, Zhihui; Man-Cho So, Anthony; Vidal, René Nonconvex robust low-rank matrix recovery. (English) Zbl 07175265 SIAM J. Optim. 30, No. 1, 660-686 (2020). MSC: 65K10 90C26 68Q25 68W40 62B10 PDFBibTeX XMLCite \textit{X. Li} et al., SIAM J. Optim. 30, No. 1, 660--686 (2020; Zbl 07175265) Full Text: DOI arXiv
Li, Xinrong; Xiu, Naihua; Zhou, Shenglong Matrix optimization over low-rank spectral sets: stationary points and local and global minimizers. (English) Zbl 1432.90124 J. Optim. Theory Appl. 184, No. 3, 895-930 (2020). MSC: 90C26 90C30 90C46 PDFBibTeX XMLCite \textit{X. Li} et al., J. Optim. Theory Appl. 184, No. 3, 895--930 (2020; Zbl 1432.90124) Full Text: DOI Link
Eftekhari, Armin; Hauser, Raphael A. Principal component analysis by optimization of symmetric functions has no spurious local optima. (English) Zbl 1430.90468 SIAM J. Optim. 30, No. 1, 439-463 (2020). MSC: 90C26 62H25 15A23 15A18 PDFBibTeX XMLCite \textit{A. Eftekhari} and \textit{R. A. Hauser}, SIAM J. Optim. 30, No. 1, 439--463 (2020; Zbl 1430.90468) Full Text: DOI arXiv
Yu, Ming; Gupta, Varun; Kolar, Mladen Recovery of simultaneous low rank and two-way sparse coefficient matrices, a nonconvex approach. (English) Zbl 1434.90161 Electron. J. Stat. 14, No. 1, 413-457 (2020). MSC: 90C26 90C90 PDFBibTeX XMLCite \textit{M. Yu} et al., Electron. J. Stat. 14, No. 1, 413--457 (2020; Zbl 1434.90161) Full Text: DOI arXiv Euclid
Gao, Wenbo; Goldfarb, Donald; Curtis, Frank E. ADMM for multiaffine constrained optimization. (English) Zbl 1428.90132 Optim. Methods Softw. 35, No. 2, 257-303 (2020). MSC: 90C26 90C30 PDFBibTeX XMLCite \textit{W. Gao} et al., Optim. Methods Softw. 35, No. 2, 257--303 (2020; Zbl 1428.90132) Full Text: DOI arXiv
Ling, Shuyang; Xu, Ruitu; Bandeira, Afonso S. On the landscape of synchronization networks: a perspective from nonconvex optimization. (English) Zbl 1427.90234 SIAM J. Optim. 29, No. 3, 1879-1907 (2019). MSC: 90C26 90C35 34D06 35B35 PDFBibTeX XMLCite \textit{S. Ling} et al., SIAM J. Optim. 29, No. 3, 1879--1907 (2019; Zbl 1427.90234) Full Text: DOI arXiv
Campos, Juan S.; Misener, Ruth; Parpas, Panos A multilevel analysis of the Lasserre hierarchy. (English) Zbl 1430.90456 Eur. J. Oper. Res. 277, No. 1, 32-41 (2019). MSC: 90C22 90C26 90C20 PDFBibTeX XMLCite \textit{J. S. Campos} et al., Eur. J. Oper. Res. 277, No. 1, 32--41 (2019; Zbl 1430.90456) Full Text: DOI
Park, Dohyung; Kyrillidis, Anastasios; Caramanis, Constantine; Sanghavi, Sujay Finding low-rank solutions via nonconvex matrix factorization, efficiently and provably. (English) Zbl 1419.90065 SIAM J. Imaging Sci. 11, No. 4, 2165-2204 (2018). MSC: 90C06 90C26 65K05 PDFBibTeX XMLCite \textit{D. Park} et al., SIAM J. Imaging Sci. 11, No. 4, 2165--2204 (2018; Zbl 1419.90065) Full Text: DOI arXiv
Zhang, Teng; Yang, Yi Robust PCA by manifold optimization. (English) Zbl 1478.62157 J. Mach. Learn. Res. 19, Paper No. 80, 39 p. (2018). MSC: 62H25 62F35 90C26 PDFBibTeX XMLCite \textit{T. Zhang} and \textit{Y. Yang}, J. Mach. Learn. Res. 19, Paper No. 80, 39 p. (2018; Zbl 1478.62157) Full Text: arXiv Link
Bonami, Pierre; Günlük, Oktay; Linderoth, Jeff Globally solving nonconvex quadratic programming problems with box constraints via integer programming methods. (English) Zbl 1400.90239 Math. Program. Comput. 10, No. 3, 333-382 (2018). MSC: 90C20 90C26 90C57 PDFBibTeX XMLCite \textit{P. Bonami} et al., Math. Program. Comput. 10, No. 3, 333--382 (2018; Zbl 1400.90239) Full Text: DOI
Hu, Jiang; Jiang, Bo; Liu, Xin; Wen, ZaiWen A note on semidefinite programming relaxations for polynomial optimization over a single sphere. (English) Zbl 1354.65123 Sci. China, Math. 59, No. 8, 1543-1560 (2016). Reviewer: Nada Djuranović-Miličić (Belgrade) MSC: 65K05 90C22 90C26 PDFBibTeX XMLCite \textit{J. Hu} et al., Sci. China, Math. 59, No. 8, 1543--1560 (2016; Zbl 1354.65123) Full Text: DOI
Shtern, Shimrit; Ben-Tal, Aharon Computational methods for solving nonconvex block-separable constrained quadratic problems. (English) Zbl 1338.90293 SIAM J. Optim. 26, No. 2, 1174-1206 (2016). MSC: 90C20 90C26 90C22 90C59 PDFBibTeX XMLCite \textit{S. Shtern} and \textit{A. Ben-Tal}, SIAM J. Optim. 26, No. 2, 1174--1206 (2016; Zbl 1338.90293) Full Text: DOI
Burer, Samuel; Kim, Sunyoung; Kojima, Masakazu Faster, but weaker, relaxations for quadratically constrained quadratic programs. (English) Zbl 1303.90077 Comput. Optim. Appl. 59, No. 1-2, 27-45 (2014). MSC: 90C20 90C26 90C22 PDFBibTeX XMLCite \textit{S. Burer} et al., Comput. Optim. Appl. 59, No. 1--2, 27--45 (2014; Zbl 1303.90077) Full Text: DOI
Wen, Zaiwen; Yin, Wotao A feasible method for optimization with orthogonality constraints. (English) Zbl 1281.49030 Math. Program. 142, No. 1-2 (A), 397-434 (2013). MSC: 49M30 49M37 90C22 90C26 90C27 90C30 65K05 PDFBibTeX XMLCite \textit{Z. Wen} and \textit{W. Yin}, Math. Program. 142, No. 1--2 (A), 397--434 (2013; Zbl 1281.49030) Full Text: DOI Link
Mitchell, John E.; Pang, Jong-Shi; Yu, Bin Obtaining tighter relaxations of mathematical programs with complementarity constraints. (English) Zbl 1346.90686 Terlaky, Tamás (ed.) et al., Modeling and optimization: Theory and applications. Selected contributions from the MOPTA 2010 conference, Bethlehem, PA, USA, August 18–20, 2010. New York, NY: Springer (ISBN 978-1-4614-3923-3/hbk; 978-1-4614-3924-0/ebook). Springer Proceedings in Mathematics & Statistics 21, 1-23 (2012). Reviewer: Igor V. Konnov (Kazan) MSC: 90C26 90C33 90C59 PDFBibTeX XMLCite \textit{J. E. Mitchell} et al., Springer Proc. Math. Stat. 21, 1--23 (2012; Zbl 1346.90686) Full Text: DOI
Bomze, Immanuel M.; Grippo, Luigi; Palagi, Laura Unconstrained formulation of standard quadratic optimization problems. (English) Zbl 1401.90141 Top 20, No. 1, 35-51 (2012). MSC: 90C20 90C26 90C30 PDFBibTeX XMLCite \textit{I. M. Bomze} et al., Top 20, No. 1, 35--51 (2012; Zbl 1401.90141) Full Text: DOI Link
Saxena, Anureet; Bonami, Pierre; Lee, Jon Convex relaxations of non-convex mixed integer quadratically constrained programs: projected formulations. (English) Zbl 1229.90144 Math. Program. 130, No. 2 (A), 359-413 (2011). MSC: 90C26 90C11 90C22 PDFBibTeX XMLCite \textit{A. Saxena} et al., Math. Program. 130, No. 2 (A), 359--413 (2011; Zbl 1229.90144) Full Text: DOI
Journée, M.; Bach, F.; Absil, P.-A.; Sepulchre, R. Low-rank optimization on the cone of positive semidefinite matrices. (English) Zbl 1215.65108 SIAM J. Optim. 20, No. 5, 2327-2351 (2010). Reviewer: Nada Djuranović-Miličić (Belgrade) MSC: 65K05 90C30 90C25 90C22 90C27 62H25 90C26 PDFBibTeX XMLCite \textit{M. Journée} et al., SIAM J. Optim. 20, No. 5, 2327--2351 (2010; Zbl 1215.65108) Full Text: DOI arXiv
Biswas, Pratik; Toh, Kim-Chuan; Ye, Yinyu A distributed SDP approach for large-scale noisy anchor-free graph realization with applications to molecular conformation. (English) Zbl 1161.49028 SIAM J. Sci. Comput. 30, No. 3, 1251-1277 (2008). MSC: 49M27 90C06 90C22 90C26 92E10 92-08 PDFBibTeX XMLCite \textit{P. Biswas} et al., SIAM J. Sci. Comput. 30, No. 3, 1251--1277 (2008; Zbl 1161.49028) Full Text: DOI
Burer, Samuel; Lee, Jon Solving maximum-entropy sampling problems using factored masks. (English) Zbl 1278.90317 Math. Program. 109, No. 2-3 (B), 263-281 (2007). MSC: 90C26 90C57 90C22 90C27 PDFBibTeX XMLCite \textit{S. Burer} and \textit{J. Lee}, Math. Program. 109, No. 2--3 (B), 263--281 (2007; Zbl 1278.90317) Full Text: DOI
Alperin, Hernán; Nowak, Ivo Lagrangian smoothing heuristics for Max-cut. (English) Zbl 1122.90426 J. Heuristics 11, No. 5-6, 447-463 (2005). MSC: 90C59 90C27 90C22 90C26 90C20 PDFBibTeX XMLCite \textit{H. Alperin} and \textit{I. Nowak}, J. Heuristics 11, No. 5--6, 447--463 (2005; Zbl 1122.90426) Full Text: DOI Link
Nowak, Ivo Relaxation and decomposition methods for mixed integer nonlinear programming. (English) Zbl 1089.90039 ISNM. International Series of Numerical Mathematics 152. Basel: Birkhäuser (ISBN 3-7643-7238-9/hbk). xvi, 213 p. (2005). Reviewer: Rainer E. Burkard (Graz) MSC: 90C11 90C30 90-02 PDFBibTeX XMLCite \textit{I. Nowak}, Relaxation and decomposition methods for mixed integer nonlinear programming. Basel: Birkhäuser (2005; Zbl 1089.90039)
Lasserre, Jean B. Semidefinite programming vs. LP relaxations for polynomial programming. (English) Zbl 1082.90554 Math. Oper. Res. 27, No. 2, 347-360 (2002). MSC: 90C22 90C09 90C26 14P99 PDFBibTeX XMLCite \textit{J. B. Lasserre}, Math. Oper. Res. 27, No. 2, 347--360 (2002; Zbl 1082.90554) Full Text: DOI Link