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 569 articles , 1 standard article )

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  1. Sun, Defeng; Toh, Kim-Chuan; Yuan, Yancheng; Zhao, Xin-Yuan: SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0) (2020)
  2. Adachi, Satoru; Nakatsukasa, Yuji: Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint (2019)
  3. Alzalg, Baha: A primal-dual interior-point method based on various selections of displacement step for symmetric optimization (2019)
  4. Amaral, Paula Alexandra; Bomze, Immanuel M.: Nonconvex min-max fractional quadratic problems under quadratic constraints: copositive relaxations (2019)
  5. Argha, Ahmadreza; Su, Steven W.; Savkin, Andrey; Celler, Branko: A framework for optimal actuator/sensor selection in a control system (2019)
  6. Beck, Amir; Guttmann-Beck, Nili: FOM -- a MATLAB toolbox of first-order methods for solving convex optimization problems (2019)
  7. Bellavia, Stefania; Gondzio, Jacek; Porcelli, Margherita: An inexact dual logarithmic barrier method for solving sparse semidefinite programs (2019)
  8. Cafuta, Kristijan: Sums of Hermitian squares decomposition of non-commutative polynomials in non-symmetric variables using NCSOStools (2019)
  9. Campos, Juan S.; Misener, Ruth; Parpas, Panos: A multilevel analysis of the Lasserre hierarchy (2019)
  10. Canelas, Alfredo; Carrasco, Miguel; López, Julio: A feasible direction algorithm for nonlinear second-order cone programs (2019)
  11. Crespo, Luis G.; Colbert, Brendon K.; Kenny, Sean P.; Giesy, Daniel P.: On the quantification of aleatory and epistemic uncertainty using sliced-normal distributions (2019)
  12. Cui, Yiran; Morikuni, Keiichi; Tsuchiya, Takashi; Hayami, Ken: Implementation of interior-point methods for LP based on Krylov subspace iterative solvers with inner-iteration preconditioning (2019)
  13. de Oliveira, Fúlvia S. S.; Souza, Fernando O.: Strong delay-independent stability of linear delay systems (2019)
  14. Faybusovich, Leonid; Zhou, Cunlu: Long-step path-following algorithm for solving symmetric programming problems with nonlinear objective functions (2019)
  15. Frot, Benjamin; Jostins, Luke; McVean, Gilean: Graphical model selection for Gaussian conditional random fields in the presence of latent variables (2019)
  16. Hippert, Benjamin; Uhde, André; Wengerek, Sascha Tobias: Portfolio benefits of adding corporate credit default swap indices: evidence from North America and Europe (2019)
  17. Hu, Shenglong: An elementary proof for the exact relaxation for rank one moment matrices in multi-polynomial SOS relaxation (2019)
  18. Hu, Shenglong; Sun, Defeng; Toh, Kim-Chuan: Best nonnegative rank-one approximations of tensors (2019)
  19. Jafari, Saeid; Ioannou, Petros A.: Reference tracking control and attenuation of unknown periodic disturbances in the presence of noise for unknown minimum-phase LTI plants (2019)
  20. Jaoude, Dany Abou; Farhood, Mazen: Coprime factors reduction of distributed nonstationary LPV systems (2019)

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