SDPT3

This software is designed to solve conic programming problems whose constraint cone is a product of semidefinite cones, second-order cones, nonnegative orthants and Euclidean spaces; and whose objective function is the sum of linear functions and log-barrier terms associated with the constraint cones. This includes the special case of determinant maximization problems with linear matrix inequalities. It employs an infeasible primal-dual predictor-corrector path-following method, with either the HKM or the NT search direction. The basic code is written in Matlab, but key subroutines in C are incorporated via Mex files. Routines are provided to read in problems in either SDPA or SeDuMi format. Sparsity and block diagonal structure are exploited. We also exploit low-rank structures in the constraint matrices associated the semidefinite blocks if such structures are explicitly given. To help the users in using our software, we also include some examples to illustrate the coding of problem data for our SQLP solver. Various techniques to improve the efficiency and stability of the algorithm are incorporated. For example, step-lengths associated with semidefinite cones are calculated via the Lanczos method. Numerical experiments show that this general purpose code can solve more than 80% of a total of about 300 test problems to an accuracy of at least 10−6 in relative duality gap and infeasibilities.


References in zbMATH (referenced in 379 articles , 1 standard article )

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  1. Bugarin, Florian; Henrion, Didier; Lasserre, Jean Bernard: Minimizing the sum of many rational functions (2016)
  2. Chen, Caihua; Liu, Yong-Jin; Sun, Defeng; Toh, Kim-Chuan: A semismooth Newton-CG based dual PPA for matrix spectral norm approximation problems (2016)
  3. Fogel, Fajwel; Waldspurger, Irène; d’Aspremont, Alexandre: Phase retrieval for imaging problems (2016)
  4. Friberg, Henrik A.: CBLIB 2014: a benchmark library for conic mixed-integer and continuous optimization (2016)
  5. Jin, Zheng-Fen; Wan, Zhongping; Jiao, Yuling; Lu, Xiliang: An alternating direction method with continuation for nonconvex low rank minimization (2016)
  6. 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 (2016)
  7. Klep, Igor; Povh, Janez: Constrained trace-optimization of polynomials in freely noncommuting variables (2016)
  8. Ling, Aifan: An inexact non-interior continuation method for semidefinite programming: convergence analysis and numerical results (2016)
  9. Liu, Ya-Feng; Diao, Rui; Ye, Feng; Liu, Hong-Wei: An efficient inexact Newton-CG algorithm for the smallest enclosing ball problem of large dimensions (2016)
  10. Li, Xianwei; Gao, Huijun; Gu, Keqin: Delay-independent stability analysis of linear time-delay systems based on frequency discretization (2016)
  11. Li, Zhengchao; Zhao, Xudong: New results on robust control for a class of uncertain systems and its applications to Chua’s oscillator (2016)
  12. Luz, Carlos J.: A characterization of the weighted Lovász number based on convex quadratic programming (2016)
  13. Ma, Jingying; Zheng, Yuanshi; Wang, Long: Topology selection for multi-agent systems with opposite leaders (2016)
  14. Mu, Cun; Zhang, Yuqian; Wright, John; Goldfarb, Donald: Scalable robust matrix recovery: Frank-Wolfe meets proximal methods (2016)
  15. Nayak, Rupaj Kumar; Desai, Jitamitra: A modified homogeneous potential reduction algorithm for solving the monotone semidefinite linear complementarity problem (2016)
  16. O’Donoghue, Brendan; Chu, Eric; Parikh, Neal; Boyd, Stephen: Conic optimization via operator splitting and homogeneous self-dual embedding (2016)
  17. Park, Sungwoo: A constraint-reduced algorithm for semidefinite optimization problems with superlinear convergence (2016)
  18. Pong, Ting Kei; Sun, Hao; Wang, Ningchuan; Wolkowicz, Henry: Eigenvalue, quadratic programming, and semidefinite programming relaxations for a cut minimization problem (2016)
  19. Simonetto, Andrea; Jamali-Rad, Hadi: Primal recovery from consensus-based dual decomposition for distributed convex optimization (2016)
  20. Van Parys, Bart P.G.; Goulart, Paul J.; Kuhn, Daniel: Generalized Gauss inequalities via semidefinite programming (2016)

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