Interior-point methods based on kernel function: theory and numerical experiments

Abstract

The aim of this thesis is to propose a primal-dual central-path interior-point method for solving linear programming problems, based on a new class of Newton directions together with a new proximity measure defined by a new kernel function. In this study, we present the main theoretical results related to interior-point methods and investigate the role of the kernel function in improving their performance, with particular emphasis on the convergence and complexity analysis of the proposed algorithm. Finally, numerical experiments are conducted to demonstrate the efficiency of the proposed algorithm.