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 697 articles , 1 standard article )

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  1. Calafiore, Giuseppe C.; Novara, Carlo; Possieri, Corrado: Control analysis and design via randomised coordinate polynomial minimisation (2022)
  2. Candogan, Utkan Onur; Chandrasekaran, Venkat: Convex graph invariant relaxations for graph edit distance (2022)
  3. Della Rossa, Matteo; Pasquini, Mirko; Angeli, David: Continuous-time switched systems with switching frequency constraints: path-complete stability criteria (2022)
  4. Doan, Xuan Vinh; Vavasis, Stephen: Low-rank matrix recovery with Ky Fan 2-(k)-norm (2022)
  5. Elbassioni, Khaled; Makino, Kazuhisa; Najy, Waleed: Finding sparse solutions for packing and covering semidefinite programs (2022)
  6. Grussler, Christian; Giselsson, Pontus: Efficient proximal mapping computation for low-rank inducing norms (2022)
  7. Lee, Jon; Skipper, Daphne; Speakman, Emily: Gaining or losing perspective (2022)
  8. Lin, Yiding; Wang, Xiang; Zhang, Lei-Hong: Solving symmetric and positive definite second-order cone linear complementarity problem by a rational Krylov subspace method (2022)
  9. Mishra, Prabhat K.; Chowdhary, Girish; Mehta, Prashant G.: Minimum variance constrained estimator (2022)
  10. Molybog, Igor; Sojoudi, Somayeh; Lavaei, Javad: Role of sparsity and structure in the optimization landscape of non-convex matrix sensing (2022)
  11. Nguyen, Viet Anh; Kuhn, Daniel; Esfahani, Peyman Mohajerin: Distributionally robust inverse covariance estimation: the Wasserstein shrinkage estimator (2022)
  12. Roig-Solvas, Biel; Sznaier, Mario: Euclidean distance bounds for linear matrix inequalities analytic centers using a novel bound on the Lambert function (2022)
  13. Rontsis, Nikitas; Goulart, Paul; Nakatsukasa, Yuji: Efficient semidefinite programming with approximate ADMM (2022)
  14. Zhang, Jingfan; Seiler, Peter; Carrasco, Joaquin: Zames-Falb multipliers for convergence rate: motivating example and convex searches (2022)
  15. Zhao, Wenjie; Zhou, Guangming: Local saddle points for unconstrained polynomial optimization (2022)
  16. Candogan, Utkan; Soh, Yong Sheng; Chandrasekeran, Venkat: A note on convex relaxations for the inverse eigenvalue problem (2021)
  17. Cavalcante, E. L. B.; Neto, E. Lucena: A pseudo-equilibrium finite element for limit analysis of Reissner-Mindlin plates (2021)
  18. Cavaleiro, Marta; Alizadeh, Farid: A dual simplex-type algorithm for the smallest enclosing ball of balls (2021)
  19. Cheng, Sheng; Martins, Nuno C.: An optimality gap test for a semidefinite relaxation of a quadratic program with two quadratic constraints (2021)
  20. Chen, Jinchi; Gao, Weiguo; Wei, Ke: Exact matrix completion based on low rank Hankel structure in the Fourier domain (2021)

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