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. Zhou, Guanglu; Toh, Kim-Chuan; Sun, Jie: Efficient algorithms for the smallest enclosing ball problem (2005)
  2. Zuluaga, Luis F.; Peña, Javier F.: A conic programming approach to generalized Tchebycheff inequalities. (2005)
  3. Anjos, Miguel F.: Proofs of unsatisfiability via semidefinite programming (2004)
  4. Anjos, Miguel F.: On semidefinite programming relaxations for the satisfiability problem (2004)
  5. Kanzow, Christian; Nagel, Christian: Corrigendum: Semidefinite programs: new search directions, smoothing-type methods, and numerical results (2004)
  6. Kuo, Yu-Ju; Mittelmann, Hans D.: Interior point methods for second-order cone programming and OR applications (2004)
  7. Todd, Michael J.: Detecting infeasibility in infeasible-interior-point methods for optimization (2004)
  8. Tsang, Ivor W.; Kwok, James T.: Efficient hyperkernel learning using second-order cone programming (2004)
  9. Yao, David D.; Zhang, Shuzhong; Zhou, Xun Yu: Stochastic linear-quadratic control via primal-dual semidefinite programming (2004)
  10. Chen, X. D.; Sun, D.; Sun, J.: Complementarity functions and numerical experiments on some smoothing Newton methods for second-order-cone complementarity problems (2003)
  11. Chen, Xin; Tseng, Paul: Non-interior continuation methods for solving semidefinite complementarity problems (2003)
  12. Kočvara, Michal; Stingl, Michael: Pennon: A code for convex nonlinear and semidefinite programming (2003)
  13. Krishnan, Kartik; Mitchell, John E.: Semi-infinite linear programming approaches to semidefinite programming problems (2003)
  14. Kumar, Piyush; Mitchell, Joseph S. B.; Yıldırım, E. Alper: Approximate minimum enclosing balls in high dimensions using core-sets (2003)
  15. Luo, Zhi-Quan: Applications of convex optimization in signal processing and digital communication (2003)
  16. Nakata, Kazuhide; Fujisawa, Katsuki; Fukuda, Mituhiro; Kojima, Masakazu; Murota, Kazuo: Exploiting sparsity in semidefinite programming via matrix completion. II: Implementation and numerical results (2003)
  17. Parrilo, Pablo A.; Lall, Sanjay: Semidefinite programming relaxations and algebraic optimization in control (2003)
  18. Sturm, Jos F.: Avoiding numerical cancellation in the interior point method for solving semidefinite programs (2003)
  19. Toh, Kim-Chuan: Solving large scale semidefinite programs via an iterative solver on the augmented systems (2003)
  20. Tütüncü, R. H.; Toh, K. C.; Todd, M. J.: Solving semidefinite-quadratic-linear programs using SDPT3 (2003)

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