Logarithmic Barrier Method Via Minorant Function for Linear Semidefinite Programming

Abstract

We propose in this study, a new logarithmic barrier approach to solve linear semidefinite programming problem. We are interested in computation of the direction by Newton’s method and of the displacement step using minorant functions instead of line search methods in order to reduce the computation cost. Our new approach is even more beneficial than classical line search methods. This purpose is confirmed by some numerical simulations showing the e˙ectiveness of the algorithm developed in this work, which are presented in the last section of this paper.

An Efficient Penalty Method without a Line Search for Nonlinear Optimization

“…A majorant function for the penalty method in convex quadratic optimization was proposed by Chaghoub and Benterki [18]. On the other hand, A. Leulmi et al [19,20] used new minorant functions for semidefinite optimization, and this idea was extended to linear programming by A. Leulmi and S. Leulmi in [21].…”