A differential equation method for solvingbox constrained variational inequality problems

Li Wang; Yang Li; Liwei Zhang

doi:10.3934/jimo.2011.7.183

Article Contents

2011, Volume 7, Issue 1: 183-198. Doi: 10.3934/jimo.2011.7.183

This issue Previous Article 2-D analysis based iterative learning control for linear discrete-time systems with time delay Next Article On the convergence rate of the inexact Levenberg-Marquardt method

A differential equation method for solving box constrained variational inequality problems

1.
School of Mathematical Sciences, Dalian University of Technology, Dalian 116024
2.
School of Sciences, Dalian Nationalities University, Dalian, 116066
3.
Department of Applied Mathematics, Dalian University of Technology, Dalian 116024, LiaoNing

Received: March 31, 2010

Revised: September 30, 2010

Published: December 2010

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Abstract

In this paper, we discuss a system of differential equations based on the projection operator for solving the box constrained variational inequality problems. The equilibrium solutions to the differential equation system are proved to be the solutions of the box constrained variational inequality problems. Two differential inclusion problems associated with the system of differential equations are introduced. It is proved that the equilibrium solution to the differential equation system is locally asymptotically stable by verifying the locally asymptotical stability of the equilibrium positions of the differential inclusion problems. An Euler discrete scheme with Armijo line search rule is introduced and its global convergence is demonstrated. The numerical experiments are reported to show that the Euler method is effective.

Keywords:

Box constrained variational inequality problem,
differential equations,
differential inclusion,
asymptotical stability,
global convergence.

Mathematics Subject Classification: Primary: 90C30, 90C33; Secondary: 65H10.

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