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. De Klerk, Etienne: Aspects of semidefinite programming. Interior point algorithms and selected applications (2002)
  2. Fukuda, Mituhiro; Kojima, Masakazu; Shida, Masayuki: Lagrangian dual interior-point methods for semidefinite programs (2002)
  3. Greenbaum, Anne: Generalizations of the field of values useful in the study of polynomial functions of a matrix (2002)
  4. Gruber, Gerald; Rendl, Franz: Computational experience with ill-posed problems in semidefinite programming (2002)
  5. Niemistö, Riitta; Dumitrescu, Bogdan; Tăbuş, Ioan: SDP design procedures for near-optimum IIR compaction filters (2002)
  6. Oliveira, S.; Stewart, D.; Soma, Takako: A subspace semidefinite programming for spectral graph partitioning (2002)
  7. Peng, Jiming; Roos, Cornelis; Terlaky, Tamás: Self-regularity: a new paradigm for primal-dual interior-point algorithms (2002)
  8. Sturm, Jos F.: Implementation of interior point methods for mixed semidefinite and second order cone optimization problems (2002)
  9. Toh, Kim-Chuan: A note on the calculation of step-lengths in interior-point methods for semidefinite programming (2002)
  10. Toh, Kim-Chuan; Kojima, Masakazu: Solving some large scale semidefinite programs via the conjugate residual method (2002)
  11. Zhang, Shao-Liang; Nakata, Kazuhide; Kojima, Masakazu: Incomplete orthogonalization preconditioners for solving large and dense linear systems which arise from semidefinite programming (2002)
  12. De Fonseca, P.; Sas, P.; Van Brussel, H.: Robust design and robust stability analysis of active noise control systems (2001)
  13. de Klerk, E.; Peng, J.; Roos, C.; Terlaky, T.: A scaled Gauss--Newton primal-dual search direction for semidefinite optimization (2001)
  14. Kim, Sunyoung; Kojima, Masakazu: Second order cone programming relaxation of nonconvex quadratic optimization problems (2001)
  15. Popeea, C.; Dumitrescu, B.: Optimal compaction gain by eigenvalue minimization. (2001)
  16. Fujisawa, Katsuki; Fukuda, Mituhiro; Kojima, Masakazu; Nakata, Kazuhide: Numerical evaluation of SDPA (semidefinite programming algorithm) (2000)
  17. Fukuda, Mituhiro; Kojima, Masakazu; Murota, Kazuo; Nakata, Kazuhide: Exploiting sparsity in semidefinite programming via matrix completion. I: General framework (2000)
  18. Sturm, Jos F.: Similarity and other spectral relations for symmetric cones (2000)
  19. Toh, Kim-Chuan: Some new search directions for primal-dual interior point methods in semidefinite programming (2000)
  20. Borchers, Brian: CSDP, a C library for semidefinite programming (1999)

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