Research About The Absolute Value Equation And The Generalized Nonlinear Complementarity Problem

This paper mainly studies the absolute value equation (AVE) and the gen-eralized nonlinear complementarity problem(GNCP) over the polyhedral cone.The structure of this paper is organized as follows.In chapter1, some definitions and notations of the absolute value equationproblem and the generalized nonlinear complementarity problem are introduced.Then, we summarize the main content of this paper.In chapter2, we discuss a kind of absolute value equation problem Ax|x|=b, A∈Rn×n, b∈Rn. We first reformulate this problem as a smoothing convexLagrange-dual programming and then suggest an efcient method for solvingit. We show that the iteration sequence generated by the proposed algorithmconverges globally in a finite iteration steps.In chapter3, we consider the generalized nonlinear complementarity problem(GNCP) over a polyhedral cone. In this paper, based on a class of smoothingfunctions, a smoothing Broyden-like algorithm is proposed for solving it. Un-der suitable conditions, the iteration sequence generated by the proposed algo-rithm converges globally and superlinearly. Furthermore, the algorithm has localquadratic convergence under mild assumptions. Some numerical experimentsshow the efciency of the proposed algorithm.