Logarithmic Barrier Method Via Minorant Function for Linear Semidefinite Programming

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.