A differential equation method for solving box constrained variational inequality problems
Li Wang, Li Yang, Liwei Zhang · Journal of Industrial and Management Optimization · 2011
In this paper, we discuss a system of differential equations basedon the projection operator for solving the box constrainedvariational inequality problems. The equilibrium solutions to thedifferential equation system are proved to be the solutions of thebox constrained variational inequality problems. Two differentialinclusion problems associated with the system of differentialequations are introduced. It is proved that the equilibriumsolution to the differential equation system is locallyasymptotically stable by verifying the locally asymptoticalstability of the equilibrium positions of the differentialinclusion problems. An Euler discrete scheme with Armijo linesearch rule is introduced and its global convergence isdemonstrated. The numerical experiments are reported to show thatthe Euler method is effective.