An Efficient Class of Modulus-Based Matrix Splitting Methods for Nonlinear Complementarity Problems

In this paper, we present an efficient method for finding a numerical solution for nonlinear complementarity problems (NCPs). We first reformulate an NCP as an equivalent system of fixed-point equations and then present a modulus-based matrix splitting iteration method. We prove the convergence of the proposed method with theorems with the relevant conditions. Our preliminary numerical results show that the method is feasible and effective.

Penalized NCP-functions for nonlinear complementarity problems and a scaling algorithm

<p style='text-indent:20px;'>In this paper, we systematically study the properties of penalized NCP-functions in derivative-free algorithms for nonlinear complementarity problems (NCPs), and give some regular conditions for stationary points of penalized NCP-functions to be solutions of NCPs. The main contribution is to unify and generalize previous results. Based on one of above penalized NCP-functions, we analyze a scaling algorithm for NCPs. The numerical results show that the scaling can greatly improve the effectiveness of the algorithm.</p>

On a Nonsmooth Gauss–Newton Algorithms for Solving Nonlinear Complementarity Problems

In this paper, we propose a new version of the generalized damped Gauss–Newton method for solving nonlinear complementarity problems based on the transformation to the nonsmooth equation, which is equivalent to some unconstrained optimization problem. The B-differential plays the role of the derivative. We present two types of algorithms (usual and inexact), which have superlinear and global convergence for semismooth cases. These results can be applied to efficiently find all solutions of the nonlinear complementarity problems under some mild assumptions. The results of the numerical tests are attached as a complement of the theoretical considerations.