A Reguarization-Newton Algorithm For The Generalized Nonlinear Complementarity Problem

In this thesis, the generalized nonlinear complementarity problem (GNCP) over a polyhedral cone is considered. To solve the problem, we first reformulate it as a system of nonlinear equations, and then we develop a regularization-Newton algorithm to solve it, the global convergence and superlinear convergence rate of the algorithm are also analyzed in this thesis.In the first chapter, we first give a simple explanation on the generalized nonlinear complementarity problem, and then we introduce some existing reformulations and existing solution methods for the problem. Some existing conclusion related to the problem are also provided.In the second chapter, we establish a new reformulation of the generalized nonlinear complementarity problem defined on a polyhedral cone (GNCP), and then we propose a regularization-Newton algorithm to solve the reformulated problem to obtain its solution. To establish superlinear convergence rate of the proposed method, we establish the condition under which the Jacobian matrix of the involved system of equation is nonsingular.