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 630 articles , 1 standard article )

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  1. Cheng, Sheng; Martins, Nuno C.: An optimality gap test for a semidefinite relaxation of a quadratic program with two quadratic constraints (2021)
  2. Henrion, Didier; Naldi, Simone; Safey El Din, Mohab: Exact algorithms for semidefinite programs with degenerate feasible set (2021)
  3. Naldi, Simone; Sinn, Rainer: Conic programming: infeasibility certificates and projective geometry (2021)
  4. Padmanabhan, Divya; Natarajan, Karthik; Murthy, Karthyek: Exploiting partial correlations in distributionally robust optimization (2021)
  5. Polyak, B. T.; Khlebnikov, M. V.; Shcherbakov, P. S.: Linear matrix inequalities in control systems with uncertainty (2021)
  6. Tanaka, Mirai; Okuno, Takayuki: Extension of the LP-Newton method to conic programming problems via semi-infinite representation (2021)
  7. Wang, Jie; Magron, Victor; Lasserre, Jean-Bernard: Chordal-TSSOS: a moment-SOS hierarchy that exploits term sparsity with chordal extension (2021)
  8. Anstreicher, Kurt M.: Efficient solution of maximum-entropy sampling problems (2020)
  9. Ariola, Marco; De Tommasi, Gianmaria; Mele, Adriano; Tartaglione, Gaetano: On the numerical solution of differential linear matrix inequalities (2020)
  10. Bruno, Hugo; Barros, Guilherme; Menezes, Ivan F. M.; Martha, Luiz Fernando: Return-mapping algorithms for associative isotropic hardening plasticity using conic optimization (2020)
  11. Chen, Xi; Lin, Qihang; Sen, Bodhisattva: On degrees of freedom of projection estimators with applications to multivariate nonparametric regression (2020)
  12. Do, Manh-Hung; Koenig, Damien; Theilliol, Didier: Robust (\mathcalH_\infty) proportional-integral observer-based controller for uncertain LPV system (2020)
  13. Eltved, Anders; Dahl, Joachim; Andersen, Martin S.: On the robustness and scalability of semidefinite relaxation for optimal power flow problems (2020)
  14. Feng, Qian; Nguang, Sing Kiong; Perruquetti, Wilfrid: Dissipative stabilization of linear systems with time-varying general distributed delays (2020)
  15. Finardi, E. C.; Lobato, R. D.; de Matos, V. L.; Sagastizábal, C.; Tomasgard, A.: Stochastic hydro-thermal unit commitment via multi-level scenario trees and bundle regularization (2020)
  16. Franzè, Giuseppe; Fedele, Giuseppe: A distributed model predictive control strategy for finite-time synchronization problems in multi-agent double-integrator systems (2020)
  17. Gaar, Elisabeth; Rendl, Franz: A computational study of exact subgraph based SDP bounds for max-cut, stable set and coloring (2020)
  18. Groetzner, Patrick; Dür, Mirjam: A factorization method for completely positive matrices (2020)
  19. Hosoe, Yohei; Peaucelle, Dimitri; Hagiwara, Tomomichi: Linearization of expectation-based inequality conditions in control for discrete-time linear systems represented with random polytopes (2020)
  20. Jarre, Florian; Lieder, Felix; Liu, Ya-Feng; Lu, Cheng: Set-completely-positive representations and cuts for the max-cut polytope and the unit modulus lifting (2020)

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