A smoothing homotopy method based on Robinson's normal equation for mixed complementarity problems

Zhengyong Zhou; Bo Yu

doi:10.3934/jimo.2011.7.977

Article Contents

2011, Volume 7, Issue 4: 977-989. Doi: 10.3934/jimo.2011.7.977

This issue Previous Article A variational problem and optimal control Next Article Multiple solutions for a class of semilinear elliptic variational inclusion problems

A smoothing homotopy method based on Robinson's normal equation for mixed complementarity problems

Zhengyong Zhou^1, and
Bo Yu^2,

1.
School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024
2.
School of Mathematical Science, Dalian University of Technology, Dalian, Liaoning 116024

Received: January 2011

Revised: June 2011

Published: October 2011

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Abstract

In this paper, a probability-one homotopy method for solving mixed complementarity problems is proposed. The homotopy equation is constructed by using the Robinson's normal equation of mixed complementarity problem and a $C^2$-smooth approximation of projection function. Under the condition that the mixed complementarity problem has no solution at infinity, which is a weaker condition than several well-known ones, existence and convergence of a smooth homotopy path from almost any starting point in $\mathbb{R}^n$ are proven. The homotopy method is implemented in Matlab and numerical results on the MCPLIB test collection are given.

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Mathematics Subject Classification: 90C33, 65D10, 65H20.

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