The SemiDefinite Programming (SDP) is not only an extension of Linear Programming (LP) but also includes convex quadratic optimization problems and some other convex optimization problems. It has a lot of applications in various fields such as combinatorial optimization, control theory, robust optimization, and quantum chemistry. In our work we present the implantation of a new algorithm for solving semidefinite programming problems. The algorithm is based on a new class of interior–exterior method. The latter is also known as the primal-dual method of type path-following where only one Newton iteration is sufficient to approximate the solution of penalized problem which satisfies a criterion of proximity. The result is demonstrated by solving problems from SDPLIB problem sets using semidefinite solver SDPA that is modified to include the interior-exterior point method subroutine. We specifically solved instances of quadratic problems. The preliminaries numerical results show the performance of this procedure and why its integration is a reasonable approach for solving semidefinite programming problems. Our future work is to implement a new variant of this method with another way to determine the step-size along the direction which is more efficient than classical line searches.
Mots clés : Interior point method, Exterior point method, Primal-dual method, Semidefinite programming, Interior–exterior approach