Solving semidefinite-quadratic-linear programs using SDPT3

Solving semidefinite-quadratic-linear programs using SDPT3

March 19, 2001 / Accepted: January 18, 2002 | R. H. Tütüncü, K. C. Toh, M. J. Todd
This paper discusses the computational experiments with linear optimization problems involving semidefinite, quadratic, and linear cone constraints (SGLPs) using a new release of SDPT3, a MATLAB implementation of infeasible primal-dual path-following algorithms. The software uses Mehrotra-type predictor-corrector variants of interior-point methods and two types of search directions: the HKM and NT directions. The paper provides a detailed discussion of implementation details and computational results on problems from the SDPLIB and DIMACS Challenge collections. The current version of SDPT3, version 3.0, is faster than previous versions, especially on large sparse problems, and can solve much larger problems. It also directly solves problems with second-order cone constraints, which was not possible in the previous version. The paper covers the primal-dual infeasible-interior-point algorithm, the computation of search directions, step-length computation, initial iterates, and implementation details. It also discusses the use of C Mex files and cell array representation for problem data. Computational experiments are presented, showing the effectiveness of the software on various test problems.This paper discusses the computational experiments with linear optimization problems involving semidefinite, quadratic, and linear cone constraints (SGLPs) using a new release of SDPT3, a MATLAB implementation of infeasible primal-dual path-following algorithms. The software uses Mehrotra-type predictor-corrector variants of interior-point methods and two types of search directions: the HKM and NT directions. The paper provides a detailed discussion of implementation details and computational results on problems from the SDPLIB and DIMACS Challenge collections. The current version of SDPT3, version 3.0, is faster than previous versions, especially on large sparse problems, and can solve much larger problems. It also directly solves problems with second-order cone constraints, which was not possible in the previous version. The paper covers the primal-dual infeasible-interior-point algorithm, the computation of search directions, step-length computation, initial iterates, and implementation details. It also discusses the use of C Mex files and cell array representation for problem data. Computational experiments are presented, showing the effectiveness of the software on various test problems.
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