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Mathematical Problems in Engineering
Volume 2013, Article ID 808965, 5 pages
http://dx.doi.org/10.1155/2013/808965
Research Article

Particle Swarm Optimization-Proximal Point Algorithm for Nonlinear Complementarity Problems

1College of Computer Science and Technology, Xi’an University of Posts and Telecommunications, Xi’an 710121, China
2College of Science, Xi’an University of Posts and Telecommunications, Xi’an 710121, China

Received 27 April 2013; Accepted 28 November 2013

Academic Editor: Jian Guo Zhou

Copyright © 2013 Chai Jun-Feng and Wang Shu-Yan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new algorithm is presented for solving the nonlinear complementarity problem by combining the particle swarm and proximal point algorithm, which is called the particle swarm optimization-proximal point algorithm. The algorithm mainly transforms nonlinear complementarity problems into unconstrained optimization problems of smooth functions using the maximum entropy function and then optimizes the problem using the proximal point algorithm as the outer algorithm and particle swarm algorithm as the inner algorithm. The numerical results show that the algorithm has a fast convergence speed and good numerical stability, so it is an effective algorithm for solving nonlinear complementarity problems.