Resolution of semidefinite linear complementarity problem (SDLCP) using new interior point methods based on kernel fonctions .

Abstract

In this thesis, we propose a new kernel function which has a great influence on the improvement of the complexity and a crucial role concerning the introduction of a new class of search directions to solve the monotone semidefinite linear complementarity problem (SDLCP) by primal-dual following path interior point algorithm. This directions are not orthogonal what makes the study more difficult. A theoretical, algorithmic and numerical study was carried out. We obtain currently best known iteration bound for the algorithm with large-update method, namely O (√n(log n) 2 log(n/ε)). The implementation of the algorithm showed a great improvement concerning the time and the number of iterations.