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 406 articles , 1 standard article )

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  1. Arima, Naohiko; Kim, Sunyoung; Kojima, Masakazu; Toh, Kim-Chuan: A robust Lagrangian-DNN method for a class of quadratic optimization problems (2017)
  2. Briat, Corentin: Dwell-time stability and stabilization conditions for linear positive impulsive and switched systems (2017)
  3. Ding, Chao; Qi, Hou-Duo: Convex optimization learning of faithful Euclidean distance representations in nonlinear dimensionality reduction (2017)
  4. Ding, Chao; Qi, Hou-Duo: Convex Euclidean distance embedding for collaborative position localization with NLOS mitigation (2017)
  5. Ducuara, Andrés F.; Susa, Cristian E.; Reina, John H.: Not-Post-Peierls compatibility under noisy channels (2017)
  6. Dumitrescu, Bogdan: Positive trigonometric polynomials and signal processing applications (2017)
  7. Lasserre, Jean B.; Toh, Kim-Chuan; Yang, Shouguang: A bounded degree SOS hierarchy for polynomial optimization (2017)
  8. Mao, Qi; Wang, Li; Tsang, Ivor W.: A unified probabilistic framework for robust manifold learning and embedding (2017)
  9. Mohammad-Nezhad, Ali; Terlaky, Tamás: A polynomial primal-dual affine scaling algorithm for symmetric conic optimization (2017)
  10. Natarajan, Karthik; Teo, Chung-Piaw: On reduced semidefinite programs for second order moment bounds with applications (2017)
  11. Nie, Jiawang; Wang, Li; Ye, Jane J.: Bilevel polynomial programs and semidefinite relaxation methods (2017)
  12. Papp, Dávid: Semi-infinite programming using high-degree polynomial interpolants and semidefinite programming (2017)
  13. Peng, Dingtao; Xiu, Naihua; Yu, Jian: $S_1/2$ regularization methods and fixed point algorithms for affine rank minimization problems (2017)
  14. Permenter, Frank; Friberg, Henrik A.; Andersen, Erling D.: Solving conic optimization problems via self-dual embedding and facial reduction: A unified approach (2017)
  15. Sakaue, Shinsaku; Takeda, Akiko; Kim, Sunyoung; Ito, Naoki: Exact semidefinite programming relaxations with truncated moment matrix for binary polynomial optimization problems (2017)
  16. Yang, Zai; Xie, Lihua: On gridless sparse methods for multi-snapshot direction of arrival estimation (2017)
  17. Amini, Amir; Azarbahram, Ali; Sojoodi, Mahdi: $H_\infty $ consensus of nonlinear multi-agent systems using dynamic output feedback controller: an LMI approach (2016)
  18. Bugarin, Florian; Henrion, Didier; Lasserre, Jean Bernard: Minimizing the sum of many rational functions (2016)
  19. Chen, Caihua; Liu, Yong-Jin; Sun, Defeng; Toh, Kim-Chuan: A semismooth Newton-CG based dual PPA for matrix spectral norm approximation problems (2016)
  20. Fantuzzi, G.; Goluskin, D.; Huang, D.; Chernyshenko, S.I.: Bounds for deterministic and stochastic dynamical systems using sum-of-squares optimization (2016)

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