Li, Xudong; Sun, Defeng; Toh, Kim-Chuan An asymptotically superlinearly convergent semismooth Newton augmented Lagrangian method for linear programming. (English) Zbl 07248645 SIAM J. Optim. 30, No. 3, 2410-2440 (2020). MSC: 90C05 90C06 90C25 65F10 PDF BibTeX XML Cite \textit{X. Li} et al., SIAM J. Optim. 30, No. 3, 2410--2440 (2020; Zbl 07248645) Full Text: DOI
Zhang, Yangjing; Zhang, Ning; Sun, Defeng; Toh, Kim-Chuan A proximal point dual Newton algorithm for solving group graphical Lasso problems. (English) Zbl 1448.90096 SIAM J. Optim. 30, No. 3, 2197-2220 (2020). MSC: 90C35 62J10 PDF BibTeX XML Cite \textit{Y. Zhang} et al., SIAM J. Optim. 30, No. 3, 2197--2220 (2020; Zbl 1448.90096) Full Text: DOI
Ding, Chao; Sun, Defeng; Sun, Jie; Toh, Kim-Chuan Spectral operators of matrices: semismoothness and characterizations of the generalized Jacobian. (English) Zbl 1434.49007 SIAM J. Optim. 30, No. 1, 630-659 (2020). MSC: 49J52 65K05 90C25 49J50 90C06 90C30 PDF BibTeX XML Cite \textit{C. Ding} et al., SIAM J. Optim. 30, No. 1, 630--659 (2020; Zbl 1434.49007) Full Text: DOI
Li, Xudong; Sun, Defeng; Toh, Kim-Chuan On the efficient computation of a generalized Jacobian of the projector over the Birkhoff polytope. (English) Zbl 1434.90116 Math. Program. 179, No. 1-2 (A), 419-446 (2020). MSC: 90C20 49J52 49M15 65F10 90C06 90C25 PDF BibTeX XML Cite \textit{X. Li} et al., Math. Program. 179, No. 1--2 (A), 419--446 (2020; Zbl 1434.90116) Full Text: DOI arXiv
Zhang, Yangjing; Zhang, Ning; Sun, Defeng; Toh, Kim-Chuan An efficient Hessian based algorithm for solving large-scale sparse group Lasso problems. (English) Zbl 1435.90112 Math. Program. 179, No. 1-2 (A), 223-263 (2020). MSC: 90C25 90C06 62J05 PDF BibTeX XML Cite \textit{Y. Zhang} et al., Math. Program. 179, No. 1--2 (A), 223--263 (2020; Zbl 1435.90112) Full Text: DOI arXiv
Sun, Defeng; Toh, Kim-Chuan; Yuan, Yancheng; Zhao, Xin-Yuan SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0). (English) Zbl 1432.90104 Optim. Methods Softw. 35, No. 1, 87-115 (2020). MSC: 90C22 PDF BibTeX XML Cite \textit{D. Sun} et al., Optim. Methods Softw. 35, No. 1, 87--115 (2020; Zbl 1432.90104) Full Text: DOI arXiv
Chen, Liang; Sun, Defeng; Toh, Kim Chuan; Zhang, Ning A unified algorithmic framework of symmetric Gauss-Seidel decomposition based proximal ADMMs for convex composite programming. (English) Zbl 07266711 J. Comput. Math. 37, No. 6, 739-757 (2019). MSC: 90C25 65K05 PDF BibTeX XML Cite \textit{L. Chen} et al., J. Comput. Math. 37, No. 6, 739--757 (2019; Zbl 07266711) Full Text: DOI
Luo, Ziyan; Sun, Defeng; Toh, Kim-Chuan; Xiu, Naihua Solving the OSCAR and SLOPE models using a semismooth Newton-based augmented Lagrangian method. (English) Zbl 1434.68430 J. Mach. Learn. Res. 20, Paper No. 106, 25 p. (2019). MSC: 68T05 62J05 62J07 PDF BibTeX XML Cite \textit{Z. Luo} et al., J. Mach. Learn. Res. 20, Paper No. 106, 25 p. (2019; Zbl 1434.68430) Full Text: Link
Chen, Liang; Sun, Defeng; Toh, Kimchuan Some problems on the Gauss-Seidel iteration method in degenerate cases. (Chinese. English summary) Zbl 1449.65052 J. Numer. Methods Comput. Appl. 40, No. 2, 98-110 (2019). MSC: 65F10 PDF BibTeX XML Cite \textit{L. Chen} et al., J. Numer. Methods Comput. Appl. 40, No. 2, 98--110 (2019; Zbl 1449.65052)
Hu, Shenglong; Sun, Defeng; Toh, Kim-Chuan Best nonnegative rank-one approximations of tensors. (English) Zbl 07141462 SIAM J. Matrix Anal. Appl. 40, No. 4, 1527-1554 (2019). MSC: 90C23 15A18 15A42 15A69 90C22 PDF BibTeX XML Cite \textit{S. Hu} et al., SIAM J. Matrix Anal. Appl. 40, No. 4, 1527--1554 (2019; Zbl 07141462) Full Text: DOI arXiv
Cui, Ying; Sun, Defeng; Toh, Kim-Chuan Computing the best approximation over the intersection of a polyhedral set and the doubly nonnegative cone. (English) Zbl 1431.90109 SIAM J. Optim. 29, No. 4, 2785-2813 (2019). MSC: 90C22 90C25 90C06 PDF BibTeX XML Cite \textit{Y. Cui} et al., SIAM J. Optim. 29, No. 4, 2785--2813 (2019; Zbl 1431.90109) Full Text: DOI arXiv
Cui, Ying; Sun, Defeng; Toh, Kim-Chuan On the R-superlinear convergence of the KKT residuals generated by the augmented Lagrangian method for convex composite conic programming. (English) Zbl 1423.90171 Math. Program. 178, No. 1-2 (A), 381-415 (2019). MSC: 90C22 90C25 90C31 65K05 PDF BibTeX XML Cite \textit{Y. Cui} et al., Math. Program. 178, No. 1--2 (A), 381--415 (2019; Zbl 1423.90171) Full Text: DOI
Lin, Meixia; Liu, Yong-Jin; Sun, Defeng; Toh, Kim-Chuan Efficient sparse semismooth Newton methods for the clustered Lasso problem. (English) Zbl 1427.90200 SIAM J. Optim. 29, No. 3, 2026-2052 (2019). MSC: 90C06 90C25 90C90 PDF BibTeX XML Cite \textit{M. Lin} et al., SIAM J. Optim. 29, No. 3, 2026--2052 (2019; Zbl 1427.90200) Full Text: DOI arXiv
Li, Xudong; Sun, Defeng; Toh, Kim-Chuan A block symmetric Gauss-Seidel decomposition theorem for convex composite quadratic programming and its applications. (English) Zbl 1412.90086 Math. Program. 175, No. 1-2 (A), 395-418 (2019). MSC: 90C06 90C20 90C25 65F10 PDF BibTeX XML Cite \textit{X. Li} et al., Math. Program. 175, No. 1--2 (A), 395--418 (2019; Zbl 1412.90086) Full Text: DOI arXiv
Li, Xudong; Sun, Defeng; Toh, Kim-Chuan QSDPNAL: a two-phase augmented Lagrangian method for convex quadratic semidefinite programming. (English) Zbl 1411.90213 Math. Program. Comput. 10, No. 4, 703-743 (2018). MSC: 90C06 90C20 90C22 90C25 65F10 PDF BibTeX XML Cite \textit{X. Li} et al., Math. Program. Comput. 10, No. 4, 703--743 (2018; Zbl 1411.90213) Full Text: DOI arXiv
Li, Xudong; Sun, Defeng; Toh, Kim-Chuan On efficiently solving the subproblems of a level-set method for fused lasso problems. (English) Zbl 1401.90145 SIAM J. Optim. 28, No. 2, 1842-1866 (2018). MSC: 90C20 90C22 90C06 90C25 PDF BibTeX XML Cite \textit{X. Li} et al., SIAM J. Optim. 28, No. 2, 1842--1866 (2018; Zbl 1401.90145) Full Text: DOI arXiv
Ding, Chao; Sun, Defeng; Sun, Jie; Toh, Kim-Chuan Spectral operators of matrices. (English) Zbl 1411.90264 Math. Program. 168, No. 1-2 (B), 509-531 (2018). Reviewer: Do Van Luu (Hanoi) MSC: 90C25 90C06 65K05 49J50 49J52 PDF BibTeX XML Cite \textit{C. Ding} et al., Math. Program. 168, No. 1--2 (B), 509--531 (2018; Zbl 1411.90264) Full Text: DOI arXiv
Li, Xudong; Sun, Defeng; Toh, Kim-Chuan A highly efficient semismooth Newton augmented Lagrangian method for solving lasso problems. (English) Zbl 1392.65062 SIAM J. Optim. 28, No. 1, 433-458 (2018). MSC: 65F10 90C06 90C25 90C31 PDF BibTeX XML Cite \textit{X. Li} et al., SIAM J. Optim. 28, No. 1, 433--458 (2018; Zbl 1392.65062) Full Text: DOI arXiv
Chen, Liang; Sun, Defeng; Toh, Kim-Chuan A note on the convergence of ADMM for linearly constrained convex optimization problems. (English) Zbl 1367.90083 Comput. Optim. Appl. 66, No. 2, 327-343 (2017). MSC: 90C25 90C46 65K05 PDF BibTeX XML Cite \textit{L. Chen} et al., Comput. Optim. Appl. 66, No. 2, 327--343 (2017; Zbl 1367.90083) Full Text: DOI arXiv
Chen, Liang; Sun, Defeng; Toh, Kim-Chuan An efficient inexact symmetric Gauss-Seidel based majorized ADMM for high-dimensional convex composite conic programming. (English) Zbl 1356.90105 Math. Program. 161, No. 1-2 (A), 237-270 (2017). MSC: 90C25 90C22 90C06 65K05 PDF BibTeX XML Cite \textit{L. Chen} et al., Math. Program. 161, No. 1--2 (A), 237--270 (2017; Zbl 1356.90105) Full Text: DOI arXiv
Cui, Ying; Li, Xudong; Sun, Defeng; Toh, Kim-Chuan On the convergence properties of a majorized alternating direction method of multipliers for linearly constrained convex optimization problems with coupled objective functions. (English) Zbl 1342.90130 J. Optim. Theory Appl. 169, No. 3, 1013-1041 (2016). MSC: 90C25 68Q25 65K05 PDF BibTeX XML Cite \textit{Y. Cui} et al., J. Optim. Theory Appl. 169, No. 3, 1013--1041 (2016; Zbl 1342.90130) Full Text: DOI
Sun, Defeng; Toh, Kim-Chuan; Yang, Liuqin An efficient inexact ABCD method for least squares semidefinite programming. (English) Zbl 1346.90658 SIAM J. Optim. 26, No. 2, 1072-1100 (2016). MSC: 90C22 90C06 90C25 65F10 PDF BibTeX XML Cite \textit{D. Sun} et al., SIAM J. Optim. 26, No. 2, 1072--1100 (2016; Zbl 1346.90658) Full Text: DOI arXiv
Li, Min; Sun, Defeng; Toh, Kim-Chuan A majorized ADMM with indefinite proximal terms for linearly constrained convex composite optimization. (English) Zbl 1338.90305 SIAM J. Optim. 26, No. 2, 922-950 (2016). MSC: 90C25 90C33 65K05 PDF BibTeX XML Cite \textit{M. Li} et al., SIAM J. Optim. 26, No. 2, 922--950 (2016; Zbl 1338.90305) Full Text: DOI arXiv
Chen, Caihua; Liu, Yong-Jin; Sun, Defeng; Toh, Kim-Chuan A semismooth Newton-CG based dual PPA for matrix spectral norm approximation problems. (English) Zbl 1342.90100 Math. Program. 155, No. 1-2 (A), 435-470 (2016). Reviewer: Rembert Reemtsen (Cottbus) MSC: 90C06 90C25 65F99 PDF BibTeX XML Cite \textit{C. Chen} et al., Math. Program. 155, No. 1--2 (A), 435--470 (2016; Zbl 1342.90100) Full Text: DOI
Li, Xudong; Sun, Defeng; Toh, Kim-Chuan A Schur complement based semi-proximal ADMM for convex quadratic conic programming and extensions. (English) Zbl 1342.90134 Math. Program. 155, No. 1-2 (A), 333-373 (2016). Reviewer: Rembert Reemtsen (Cottbus) MSC: 90C25 90C22 90C20 90C06 65F10 PDF BibTeX XML Cite \textit{X. Li} et al., Math. Program. 155, No. 1--2 (A), 333--373 (2016; Zbl 1342.90134) Full Text: DOI arXiv
Li, Min; Sun, Defeng; Toh, Kim-Chuan A convergent 3-block semi-proximal ADMM for convex minimization problems with one strongly convex block. (English) Zbl 1327.90214 Asia-Pac. J. Oper. Res. 32, No. 4, Article ID 1550024, 19 p. (2015). MSC: 90C25 90C33 65K05 PDF BibTeX XML Cite \textit{M. Li} et al., Asia-Pac. J. Oper. Res. 32, No. 4, Article ID 1550024, 19 p. (2015; Zbl 1327.90214) Full Text: DOI arXiv
Yang, Liuqin; Sun, Defeng; Toh, Kim-Chuan SDPNAL+: a majorized semismooth Newton-CG augmented Lagrangian method for semidefinite programming with nonnegative constraints. (English) Zbl 1321.90085 Math. Program. Comput. 7, No. 3, 331-366 (2015). MSC: 90C06 90C22 90C25 65F10 PDF BibTeX XML Cite \textit{L. Yang} et al., Math. Program. Comput. 7, No. 3, 331--366 (2015; Zbl 1321.90085) Full Text: DOI arXiv
Sun, Defeng; Toh, Kim-Chuan; Yang, Liuqin A convergent 3-block semiproximal alternating direction method of multipliers for conic programming with 4-type constraints. (English) Zbl 1328.90083 SIAM J. Optim. 25, No. 2, 882-915 (2015). MSC: 90C06 90C22 90C25 65F10 PDF BibTeX XML Cite \textit{D. Sun} et al., SIAM J. Optim. 25, No. 2, 882--915 (2015; Zbl 1328.90083) Full Text: DOI arXiv
Jiang, Kaifeng; Sun, Defeng; Toh, Kim-Chuan A partial proximal point algorithm for nuclear norm regularized matrix least squares problems. (English) Zbl 1327.90109 Math. Program. Comput. 6, No. 3, 281-325 (2014). MSC: 90C06 90C22 90C25 65F10 PDF BibTeX XML Cite \textit{K. Jiang} et al., Math. Program. Comput. 6, No. 3, 281--325 (2014; Zbl 1327.90109) Full Text: DOI
Wu, Bin; Ding, Chao; Sun, Defeng; Toh, Kim-Chuan On the Moreau-Yosida regularization of the vector \(k\)-norm related functions. (English) Zbl 1297.90122 SIAM J. Optim. 24, No. 2, 766-794 (2014). MSC: 90C25 90C30 65K05 49J52 PDF BibTeX XML Cite \textit{B. Wu} et al., SIAM J. Optim. 24, No. 2, 766--794 (2014; Zbl 1297.90122) Full Text: DOI
Ding, Chao; Sun, Defeng; Toh, Kim-Chuan An introduction to a class of matrix cone programming. (English) Zbl 1301.65043 Math. Program. 144, No. 1-2 (A), 141-179 (2014). Reviewer: Nada Djuranović-Miličić (Belgrade) MSC: 65K05 90C25 90C30 90C22 90C06 PDF BibTeX XML Cite \textit{C. Ding} et al., Math. Program. 144, No. 1--2 (A), 141--179 (2014; Zbl 1301.65043) Full Text: DOI
Yang, Junfeng; Sun, Defeng; Toh, Kim-Chuan A proximal point algorithm for log-determinant optimization with group Lasso regularization. (English) Zbl 1285.65037 SIAM J. Optim. 23, No. 2, 857-893 (2013). Reviewer: Andrea Walther (Paderborn) MSC: 65K05 90C15 90C53 PDF BibTeX XML Cite \textit{J. Yang} et al., SIAM J. Optim. 23, No. 2, 857--893 (2013; Zbl 1285.65037) Full Text: DOI
Jiang, Kaifeng; Sun, Defeng; Toh, Kim-Chuan Solving nuclear norm regularized and semidefinite matrix least squares problems with linear equality constraints. (English) Zbl 1297.90085 Bezdek, Károly (ed.) et al., Discrete geometry and optimization. Selected papers based on the presentations at the conference and workshop, Toronto, Canada, September 19–23, 2011. New York, NY: Springer (ISBN 978-3-319-00199-9/hbk; 978-3-319-00200-2/ebook). Fields Institute Communications 69, 133-162 (2013). MSC: 90C06 90C22 90C25 65F10 PDF BibTeX XML Cite \textit{K. Jiang} et al., Fields Inst. Commun. 69, 133--162 (2013; Zbl 1297.90085) Full Text: DOI
Jiang, Kaifeng; Sun, Defeng; Toh, Kim-Chuan An inexact accelerated proximal gradient method for large scale linearly constrained convex SDP. (English) Zbl 1401.90120 SIAM J. Optim. 22, No. 3, 1042-1064 (2012). MSC: 90C06 90C22 90C25 65F10 PDF BibTeX XML Cite \textit{K. Jiang} et al., SIAM J. Optim. 22, No. 3, 1042--1064 (2012; Zbl 1401.90120) Full Text: DOI
Liu, Yong-Jin; Sun, Defeng; Toh, Kim-Chuan An implementable proximal point algorithmic framework for nuclear norm minimization. (English) Zbl 1262.90125 Math. Program. 133, No. 1-2 (A), 399-436 (2012). Reviewer: Jean-Jacques Strodiot (Namur) MSC: 90C22 46N10 65K05 90C25 PDF BibTeX XML Cite \textit{Y.-J. Liu} et al., Math. Program. 133, No. 1--2 (A), 399--436 (2012; Zbl 1262.90125) Full Text: DOI
Wang, Chengjing; Sun, Defeng; Toh, Kim-Chuan Solving log-determinant optimization problems by a Newton-CG primal proximal point algorithm. (English) Zbl 1211.90130 SIAM J. Optim. 20, No. 6, 2994-3013 (2010). MSC: 90C06 90C22 90C25 65F10 PDF BibTeX XML Cite \textit{C. Wang} et al., SIAM J. Optim. 20, No. 6, 2994--3013 (2010; Zbl 1211.90130) Full Text: DOI
Zhao, Xin-Yuan; Sun, Defeng; Toh, Kim-Chuan A Newton-CG augmented Lagrangian method for semidefinite programming. (English) Zbl 1213.90175 SIAM J. Optim. 20, No. 4, 1737-1765 (2010). Reviewer: Rembert Reemtsen (Cottbus) MSC: 90C06 90C22 90C25 65F10 PDF BibTeX XML Cite \textit{X.-Y. Zhao} et al., SIAM J. Optim. 20, No. 4, 1737--1765 (2010; Zbl 1213.90175) Full Text: DOI