Tang, Tianyun; Toh, Kim-Chuan Solving graph equipartition SDPs on an algebraic variety. (English) Zbl 07807811 Math. Program. 204, No. 1-2 (A), 299-347 (2024). MSC: 90C06 90C22 90C27 PDFBibTeX XMLCite \textit{T. Tang} and \textit{K.-C. Toh}, Math. Program. 204, No. 1--2 (A), 299--347 (2024; Zbl 07807811) Full Text: DOI arXiv
Yang, Heng; Liang, Ling; Carlone, Luca; Toh, Kim-Chuan An inexact projected gradient method with rounding and lifting by nonlinear programming for solving rank-one semidefinite relaxation of polynomial optimization. (English) Zbl 1522.90033 Math. Program. 201, No. 1-2 (A), 409-472 (2023). MSC: 90C06 90C22 90C23 90C55 PDFBibTeX XMLCite \textit{H. Yang} et al., Math. Program. 201, No. 1--2 (A), 409--472 (2023; Zbl 1522.90033) Full Text: DOI arXiv
Lin, Meixia; Sun, Defeng; Toh, Kim-Chuan An augmented Lagrangian method with constraint generation for shape-constrained convex regression problems. (English) Zbl 1489.90060 Math. Program. Comput. 14, No. 2, 223-270 (2022). MSC: 90C06 90C25 90C90 PDFBibTeX XMLCite \textit{M. Lin} et al., Math. Program. Comput. 14, No. 2, 223--270 (2022; Zbl 1489.90060) Full Text: DOI arXiv
Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan Doubly nonnegative relaxations for quadratic and polynomial optimization problems with binary and box constraints. (English) Zbl 1494.90071 Math. Program. 193, No. 2 (B), 761-787 (2022). MSC: 90C23 90C25 90C26 PDFBibTeX XMLCite \textit{S. Kim} et al., Math. Program. 193, No. 2 (B), 761--787 (2022; Zbl 1494.90071) Full Text: DOI
Tran-Dinh, Quoc; Liang, Ling; Toh, Kim-Chuan A new homotopy proximal variable-metric framework for composite convex minimization. (English) Zbl 1498.90159 Math. Oper. Res. 47, No. 1, 508-539 (2022). Reviewer: Yisheng Song (Hong Kong) MSC: 90C25 90C31 90C06 90-08 PDFBibTeX XMLCite \textit{Q. Tran-Dinh} et al., Math. Oper. Res. 47, No. 1, 508--539 (2022; Zbl 1498.90159) Full Text: DOI arXiv
Yang, Lei; Li, Jia; Sun, Defeng; Toh, Kim-Chuan A fast globally linearly convergent algorithm for the computation of Wasserstein barycenters. (English) Zbl 07370538 J. Mach. Learn. Res. 22, Paper No. 21, 37 p. (2021). MSC: 68T05 PDFBibTeX XMLCite \textit{L. Yang} et al., J. Mach. Learn. Res. 22, Paper No. 21, 37 p. (2021; Zbl 07370538) Full Text: arXiv Link
Hu, Shenglong; Sun, Defeng; Toh, Kim-Chuan Best nonnegative rank-one approximations of tensors. (English) Zbl 1454.90047 SIAM J. Matrix Anal. Appl. 40, No. 4, 1527-1554 (2019). MSC: 90C23 15A18 15A42 15A69 90C22 PDFBibTeX XMLCite \textit{S. Hu} et al., SIAM J. Matrix Anal. Appl. 40, No. 4, 1527--1554 (2019; Zbl 1454.90047) Full Text: DOI arXiv
Lam, Xin Yee; Marron, J. S.; Sun, Defeng; Toh, Kim-Chuan Fast algorithms for large-scale generalized distance weighted discrimination. (English) Zbl 07498954 J. Comput. Graph. Stat. 27, No. 2, 368-379 (2018). MSC: 62-XX PDFBibTeX XMLCite \textit{X. Y. Lam} et al., J. Comput. Graph. Stat. 27, No. 2, 368--379 (2018; Zbl 07498954) Full Text: DOI arXiv
Arima, Naohiko; Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan A robust Lagrangian-DNN method for a class of quadratic optimization problems. (English) Zbl 1366.90152 Comput. Optim. Appl. 66, No. 3, 453-479 (2017). MSC: 90C20 90C25 90C26 PDFBibTeX XMLCite \textit{N. Arima} et al., Comput. Optim. Appl. 66, No. 3, 453--479 (2017; Zbl 1366.90152) Full Text: DOI
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 PDFBibTeX XMLCite \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 PDFBibTeX XMLCite \textit{Y. Cui} et al., J. Optim. Theory Appl. 169, No. 3, 1013--1041 (2016; Zbl 1342.90130) 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 PDFBibTeX XMLCite \textit{M. Li} et al., SIAM J. Optim. 26, No. 2, 922--950 (2016; Zbl 1338.90305) Full Text: DOI arXiv
Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan A Lagrangian-DNN relaxation: a fast method for computing tight lower bounds for a class of quadratic optimization problems. (English) Zbl 1342.90123 Math. Program. 156, No. 1-2 (A), 161-187 (2016). MSC: 90C20 90C25 90C26 PDFBibTeX XMLCite \textit{S. Kim} et al., Math. Program. 156, No. 1--2 (A), 161--187 (2016; Zbl 1342.90123) 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 PDFBibTeX XMLCite \textit{X. Li} et al., Math. Program. 155, No. 1--2 (A), 333--373 (2016; Zbl 1342.90134) 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 PDFBibTeX XMLCite \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 PDFBibTeX XMLCite \textit{D. Sun} et al., SIAM J. Optim. 25, No. 2, 882--915 (2015; Zbl 1328.90083) Full Text: DOI arXiv
Toh, Kim-Chuan; Todd, Michael J.; Tütüncü, Reha H. On the implementation and usage of SDPT3 – a Matlab software package for semidefinite-quadratic-linear programming, version 4.0. (English) Zbl 1334.90117 Anjos, Miguel F. (ed.) et al., Handbook on semidefinite, conic and polynomial optimization. New York, NY: Springer (ISBN 978-1-4614-0768-3/hbk; 978-1-4614-0769-0/ebook). International Series in Operations Research & Management Science 166, 715-754 (2012). MSC: 90C22 90C20 90C05 90-04 PDFBibTeX XMLCite \textit{K.-C. Toh} et al., Int. Ser. Oper. Res. Manag. Sci. 166, 715--754 (2012; Zbl 1334.90117) Full Text: DOI Link
Zhou, Guanglu; Toh, Kim-Chuan; Sun, Jie Efficient algorithms for the smallest enclosing ball problem. (English) Zbl 1112.90060 Comput. Optim. Appl. 30, No. 2, 147-160 (2005). MSC: 90C25 65D18 PDFBibTeX XMLCite \textit{G. Zhou} et al., Comput. Optim. Appl. 30, No. 2, 147--160 (2005; Zbl 1112.90060) Full Text: DOI
Zhou, G.; Toh, K. C.; Sun, D. Globally and quadratically convergent algorithm for minimizing the sum of Euclidean norms. (English) Zbl 1055.90057 J. Optimization Theory Appl. 119, No. 2, 357-377 (2003). MSC: 90C20 65K05 90C33 PDFBibTeX XMLCite \textit{G. Zhou} et al., J. Optim. Theory Appl. 119, No. 2, 357--377 (2003; Zbl 1055.90057) Full Text: DOI
Toh, K. C.; Todd, M. J.; Tütüncü, R. H. SDPT3 – a MATLAB software package for semidefinite programming, version 1. 3. (English) Zbl 0997.90060 Optim. Methods Softw. 11-12, No. 1-4, 545-581 (1999). Reviewer: Klaus Schittkowski (Bayreuth) MSC: 90C22 65Y15 65K05 PDFBibTeX XMLCite \textit{K. C. Toh} et al., Optim. Methods Softw. 11--12, No. 1--4, 545--581 (1999; Zbl 0997.90060) Full Text: DOI