General Dynamical Systems and Variational Inequalities
Abstract
In this paper, we introduce and consider a new second order dynamical system for solving general variational inequalities. Using the forward backward finite difference schemes, we suggest some new multi-step
iterative methods for solving the variational inequalities and their variants forms. Convergence analysis is investigated under certain mild conditions. We also use the change of variable method to establish the equivalence between the complementarity problems and the fixed point problems. The alternate formulation can exploited to consider the dynamical systems and study the stability properties of the solution. Since the variational inequalities are equivalent to the complementarity problems, our results can be used to develop new techniques for them. It is an interesting problem to compare these methods with other technique for solving variational inequalities and related optimizations for further research activities.
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