Logarithmic Barrier Interior Point Method for Linearly Constrained Convex Programming

Abstract

In this thesis, we are interested in the linearly constrained convex optimization problem. In the first part, we present a weighted logarithmic barrier method followed by a study of convergence, the efficiency of the proposed method is shown by presenting numerical experiments. In the second part, we propose a primal-dual method to solving convex quadratic programming, the technique of majorant function is used to compute the step size, this work is enriched by important numerical simulations.