Numerical Experiments with a Primal-Dual Algorithm for Solving Quadratic Problems

Abstract

This paper provides a new variant of primal-dual interior-point method for solving a SemiDefinite Program (SDP). We use the PDIPA (primal-dual interior-point algorithm) solver entitled SDPA (SemiDefinite Programming Algorithm). This last uses a classical Newton descent method to compute the predictorcorrector search direction. The difficulty is in the computation of this line-search, it induces high computational costs. Here, instead we adopt a new procedure to implement another way to determine the step-size along the direction which is more efficient than classical line searches. This procedure consists in the computation of the step size in order to give a significant decrease along the descent line direction with a minimum cost. With this procedure we obtain à new variant of SDPA. The comparison of the results obtained with the classic SDPA and our new variant is promising.