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 481 articles , 1 standard article )

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  1. Behrends, Sönke; Hübner, Ruth; Schöbel, Anita: Norm bounds and underestimators for unconstrained polynomial integer minimization (2018)
  2. Bhim, Louis: Polynomial bounds for solutions to boundary value and obstacle problems with applications to financial derivative pricing. (Abstract of thesis) (2018)
  3. Bhim, Louis; Kawai, Reiichiro: Smooth upper bounds for the price function of American style options (2018)
  4. Campos, Juan S.; Parpas, Panos: A multigrid approach to SDP relaxations of sparse polynomial optimization problems (2018)
  5. Candogan, Utkan Onur; Chandrasekaran, Venkat: Finding planted subgraphs with few eigenvalues using the Schur-Horn relaxation (2018)
  6. de Oliveira Souza, Fernando; de Oliveira, Maurício Carvalho; Martinez Palhares, Reinaldo: A simple necessary and sufficient LMI condition for the strong delay-independent stability of LTI systems with single delay (2018)
  7. Gillis, Nicolas; Sharma, Punit: Finding the nearest positive-real system (2018)
  8. Gillis, Nicolas; Sharma, Punit: A semi-analytical approach for the positive semidefinite Procrustes problem (2018)
  9. Goluskin, David: Bounding averages rigorously using semidefinite programming: mean moments of the Lorenz system (2018)
  10. Halická, Margaréta; Trnovská, Mária: The Russell measure model: computational aspects, duality, and profit efficiency (2018)
  11. Hand, Paul; Lee, Choongbum; Voroninski, Vladislav: Exact simultaneous recovery of locations and structure from known orientations and corrupted point correspondences (2018)
  12. Huang, Zheng-Hai; Qi, Liqun: Positive definiteness of paired symmetric tensors and elasticity tensors (2018)
  13. Jarre, Florian; Lieder, Felix: The solution of Euclidean norm trust region SQP subproblems via second-order cone programs: an overview and elementary introduction (2018)
  14. Josz, Cédric; Molzahn, Daniel K.: Lasserre hierarchy for large scale polynomial optimization in real and complex variables (2018)
  15. Kaiser, Eurika; Morzyński, Marek; Daviller, Guillaume; Kutz, J. Nathan; Brunton, Bingni W.; Brunton, Steven L.: Sparsity enabled cluster reduced-order models for control (2018)
  16. Lazar, Aurel A.; Ukani, Nikul H.; Zhou, Yiyin: Sparse functional identification of complex cells from spike times and the decoding of visual stimuli (2018)
  17. Lu, Jianbo; Xi, Yugeng; Li, Dewei; Xu, Yuli; Gan, Zhongxue: Model predictive control design for polytopic uncertain systems by synthesising multi-step prediction scenarios (2018)
  18. Mishra, Prabhat K.; Chatterjee, Debasish; Quevedo, Daniel E.: Sparse and constrained stochastic predictive control for networked systems (2018)
  19. Mizutani, Tomohiko; Tanaka, Mirai: Efficient preconditioning for noisy separable nonnegative matrix factorization problems by successive projection based low-rank approximations (2018)
  20. Natarajan, Karthik; Shi, Dongjian; Toh, Kim-Chuan: Bounds for random binary quadratic programs (2018)

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