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Semidefinite programming (SDP)
has become an extremely active subject in the field of optimization/mathematical programming. It consists in minimizing/maximizing a linear objective function restricted to linear constraints on the cone of positive semidefinite symmetric matrices. Besides its interesting theoretical properties, some eminently practical applications in control theory, combinatorial optimization, algebra, quantum information, quantum chemistry, etc., have enhanced a tremendous interest in SDP. Through this website, we would like to contribute with useful information on SDPs to students and experts who have interest in this field.

This home page provides the following software packages in C++ language for solving SDPs:

  • "SDPA (SemiDefinite Programming Algorithm)"

    is one of the most efficient and stable software packages for solving SDPs based on the primal-dual interior-point method. It fully exploits the sparsity of given problems. There are some variants of the SDPA;

  • SDPA-M

    (SDPA with MATLAB interface);

  • SDPA-C

    (SDPA with the positive definite matrix Completion);

  • SDPARA

    (SDPA paRAllel version);

  • SDPARA-C

    (parallel version of the SDPA-C).

  • SDPA-GMP

    (SDPA with arbitrary precision arithmetic);

  • SDPA-QD

    (SDPA with pseudo quad-double precision arithmetic);

  • SDPA-DD

    (SDPA with pseudo double-double precision arithmetic);

  • SDPA-P

    (SDPA with Python interface);

You can download free of charge and use any of these software packages according to the sparsity and the size of your SDP problem.

The Online Solver provides a server system to the SDPA software package family to solve SDPs transmitted through the Internet. It is expected to enable users from all around of the world to utilize the SDPA and its variants, in particular, its parallel version, the SDPARA.