Study Of The Interior Point Algorithm For The Generalized Complementarity Problem

In this thesis,we mainly consider the interior point algorithm for the generalized linear complementarity problem(GLCP),the generalized nonlinear complementarity problem over a polyhedral cone.The paper consists of three Chapters.Chapter 1 gives an introduction of the thesis,which mainly discusses the current development of our concerned problem,i.e.,the generalized complementarity problem over a polyhedral cone,and the main contribution of this paper is also listed in this chapter.In Chapter 2,we propose a predictor-corrector interior point algorithm for the generalized linear complementarity problem over a polyhedral cone.To this end,we first reformulate GLCP as a standard convex quadratic problem,then establish the relationship between the solution of the GLCP and the convex quadratic problem under some assumptions;finally,we establish a predictor-corrector interior point algorithm for the convex quadratic problem and prove the quadratic convergence of the proposed method.In Chapter 3,we present a path-following perturbation Newton interior point algorithm for the generalized nonlinear complementarity problem over a polyhedral cone.For the generalized nonlinear complementarity problem over a polyhedral cone,we first reformulate it as the constrained nonlinear equations problem, then we give a path-following perturbation Newton interior point algorithm for the constrained nonlinear equations problem.The superlinear convergence of the proposed method is also established.