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 393 articles , 1 standard article )

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  1. Arima, Naohiko; Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan: A robust Lagrangian-DNN method for a class of quadratic optimization problems (2017)
  2. Ding, Chao; Qi, Hou-Duo: Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation (2017)
  3. Lasserre, Jean B.; Toh, Kim-Chuan; Yang, Shouguang: A bounded degree SOS hierarchy for polynomial optimization (2017)
  4. Mohammad-Nezhad, Ali; Terlaky, Tamás: A polynomial primal-dual affine scaling algorithm for symmetric conic optimization (2017)
  5. Natarajan, Karthik; Teo, Chung-Piaw: On reduced semidefinite programs for second order moment bounds with applications (2017)
  6. Sakaue, Shinsaku; Takeda, Akiko; Kim, Sunyoung; Ito, Naoki: Exact semidefinite programming relaxations with truncated moment matrix for binary polynomial optimization problems (2017)
  7. Amini, Amir; Azarbahram, Ali; Sojoodi, Mahdi: $H_\infty $ consensus of nonlinear multi-agent systems using dynamic output feedback controller: an LMI approach (2016)
  8. Bugarin, Florian; Henrion, Didier; Lasserre, Jean Bernard: Minimizing the sum of many rational functions (2016)
  9. Chen, Caihua; Liu, Yong-Jin; Sun, Defeng; Toh, Kim-Chuan: A semismooth Newton-CG based dual PPA for matrix spectral norm approximation problems (2016)
  10. Fantuzzi, G.; Goluskin, D.; Huang, D.; Chernyshenko, S.I.: Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization (2016)
  11. Fogel, Fajwel; Waldspurger, Irène; d’Aspremont, Alexandre: Phase retrieval for imaging problems (2016)
  12. Friberg, Henrik A.: CBLIB 2014: a benchmark library for conic mixed-integer and continuous optimization (2016)
  13. Jiang, Jun-Zheng; Zhou, Fang; Shui, Peng-Lang: Optimization design of two-channel biorthogonal graph filter banks (2016) ioport
  14. Jin, Zheng-Fen; Wan, Zhongping; Jiao, Yuling; Lu, Xiliang: An alternating direction method with continuation for nonconvex low rank minimization (2016)
  15. 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)
  16. Klep, Igor; Povh, Janez: Constrained trace-optimization of polynomials in freely noncommuting variables (2016)
  17. Kuntz, Juan; Ottobre, Michela; Stan, Guy-Bart; Barahona, Mauricio: Bounding stationary averages of polynomial diffusions via semidefinite programming (2016)
  18. Ling, Aifan: An inexact non-interior continuation method for semidefinite programming: convergence analysis and numerical results (2016)
  19. 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)
  20. Li, Xianwei; Gao, Huijun; Gu, Keqin: Delay-independent stability analysis of linear time-delay systems based on frequency discretization (2016)

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