American Institute of Mathematical Sciences

January  2011, 7(1): 183-198. doi: 10.3934/jimo.2011.7.183

A differential equation method for solving box constrained variational inequality problems

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

Received  April 2010 Revised  October 2010 Published  January 2011

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.
Citation: Li Wang, Yang Li, Liwei Zhang. A differential equation method for solving box constrained variational inequality problems. Journal of Industrial & Management Optimization, 2011, 7 (1) : 183-198. doi: 10.3934/jimo.2011.7.183
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