On some algorithmic aspects of a new projection method to solve the linear complementarity problem

Abstract

As the linear complementarity problem (LCP) is considered as one of the most interesting particular cases of the of variational inequalities problem (VIP), the objective of this dissertation is the presentation of theoretical and numerical study of two projection methods to solve this problem. The first is the projection method introduced by Ye and proposed specifically for the resolution of a generalized variational inequalities problem that we will adapt it for solving (LCP). The second one is a modified version of Ye's method where some algorithmic modifications are introduced with an aim to improve more the numerical performance of first method. A detailed description of the corresponding algorithms is given, and their convergence results are well established. The results obtained from the numerical study allowed us to give some conclusions concerning the behaviors of the two methods proposed for solving (LCP).