Logarithmic barrier and inverse barrier interior point methods in nonlinear programming

Abstract

In this thesis, we are interested in the theoretical and numerical study of some interior point methods in convex optimization problems.In the first,we propose a logarithmic barrier approach in which the penalty term is taken as a vector,followed by a convergence study where the step size is determined using a majorant function technique.In addition,we extend an inverse barrier in the nonlinear case,the step size is determined with a tangent technique.We finish this work by an extension of Karmarkar’s algorithm in nonlinear case,and this by using the linearization and translation of objective function. In all of these work,the descent direction is calculated with the classical Newton method.This study is supported by numerical tests which show the effectiveness of these approaches.