Logarithmic Barrier Interior Point Method for Linearly Constrained Convex Programming

Abstract

In this thesis,we are interested solving 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.