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.
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References in zbMATH (referenced in 602 articles , 1 standard article )
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- Mohammad-Nezhad, Ali; Terlaky, Tamás: Parametric analysis of semidefinite optimization (2020)
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- Qian, Xun; Liao, Li-Zhi; Sun, Jie: A strategy of global convergence for the affine scaling algorithm for convex semidefinite programming (2020)
- Safarina, Sena; Moriguchi, Satoko; Mullin, Tim J.; Yamashita, Makoto: Conic relaxation approaches for equal deployment problems (2020)
- Schürmann, Bastian; Vignali, Riccardo; Prandini, Maria; Althoff, Matthias: Set-based control for disturbed piecewise affine systems with state and actuation constraints (2020)
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- Sun, Defeng; Toh, Kim-Chuan; Yuan, Yancheng; Zhao, Xin-Yuan: SDPNAL+: A Matlab software for semidefinite programming with bound constraints (version 1.0) (2020)