Error Bounds and Merit Functions for Exponentially General Variational Inequalities

Abstract

In this paper, some new classes of classes of exponentially general variational inequalities are introduced. It is shown that the odd-order and nonsymmetric exponentially boundary value problems can be studied in the framework of exponentially general variational inequalities. We consider some classes of merit functions for exponentially general variational inequalities. Using these functions, we derive error bounds for the solution of exponentially general variational inequalities under some mild conditions. Since the exponentially general variational inequalities include general variational inequalities, quasi-variational inequalities and complementarity problems as special cases, results proved in this paper hold for these problems. Results obtained in this paper represent a refinement of previously known results for several classes of variational inequalities and related optimization problems.