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 523 articles , 1 standard article )

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  1. Adachi, Satoru; Nakatsukasa, Yuji: Eigenvalue-based algorithm and analysis for nonconvex QCQP with one constraint (2019)
  2. Beck, Amir; Guttmann-Beck, Nili: FOM -- a MATLAB toolbox of first-order methods for solving convex optimization problems (2019)
  3. Cafuta, Kristijan: Sums of Hermitian squares decomposition of non-commutative polynomials in non-symmetric variables using NCSOStools (2019)
  4. Campos, Juan S.; Misener, Ruth; Parpas, Panos: A multilevel analysis of the Lasserre hierarchy (2019)
  5. 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)
  6. Luo, Hezhi; Bai, Xiaodi; Peng, Jiming: Enhancing semidefinite relaxation for quadratically constrained quadratic programming via penalty methods (2019)
  7. Papp, Dávid; Yildiz, Sercan: Sum-of-squares optimization without semidefinite programming (2019)
  8. Rego, Brenner S.; Raffo, Guilherme V.: Suspended load path tracking control using a tilt-rotor UAV based on zonotopic state estimation (2019)
  9. Yu, Yongchao; Peng, Jigen; Yue, Shigang: A new nonconvex approach to low-rank matrix completion with application to image inpainting (2019)
  10. Abou Jaoude, Dany; Farhood, Mazen: Model reduction of distributed nonstationary LPV systems (2018)
  11. Adam Rahman: sdpt3r: Semidefinite Quadratic Linear Programming in R (2018) not zbMATH
  12. Anstreicher, Kurt M.: Maximum-entropy sampling and the Boolean quadric polytope (2018)
  13. Argha, Ahmadreza; Li, Li; Su, Steven W.; Nguyen, Hung: Sparsely distributed sliding mode control for interconnected systems (2018)
  14. Aßmann, Denis; Liers, Frauke; Stingl, Michael; Vera, Juan C.: Deciding robust feasibility and infeasibility using a set containment approach: an application to stationary passive gas network operations (2018)
  15. Behrends, Sönke; Hübner, Ruth; Schöbel, Anita: Norm bounds and underestimators for unconstrained polynomial integer minimization (2018)
  16. Bhim, Louis: Polynomial bounds for solutions to boundary value and obstacle problems with applications to financial derivative pricing. (Abstract of thesis) (2018)
  17. Bhim, Louis; Kawai, Reiichiro: Smooth upper bounds for the price function of American style options (2018)
  18. Bykov, A. V.; Shcherbakov, P. S.: Sparse feedback design in discrete-time linear systems (2018)
  19. Campos, Juan S.; Parpas, Panos: A multigrid approach to SDP relaxations of sparse polynomial optimization problems (2018)
  20. Candogan, Utkan Onur; Chandrasekaran, Venkat: Finding planted subgraphs with few eigenvalues using the Schur-Horn relaxation (2018)

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