Gauss-Newton Methods for the Nonlinear Complementarity Problem

摘要

It is a result of Mangasarian that the nonlinear complementarity problem is equivalent to the solution of a system of nonlinear equations. This paper considers the solution of this system by the damped Gauss-Newton method using the principle of least squares minimization. Algorithms are developed which under fairly simple conditions converge locally to a solution and under stronger hypotheses converge locally quadratically. The algorithms have been used successfully to solve both linear and nonlinear complementarity problems including a standard difficult test problem due to Colville. (Author)