Auxiliary Principle Technique For A Class OfNonlinear Variational Inequalities

Abstract

It is well known that moving, free, obstacle, unilateral, general equilibrium problems arising in elasticity, fluid flow through porous media, economics, transportation, pure and applied sciences can be studied in a unified general framework of variational inequalities. The ideas and techniques of variational inequalities are being applied in a variety of diverse fields and proved to be productive and innovative. One of the most difficult and important problems in this theory is the development of an efficient and implementable numerical method for solving these variational inequalities. In this paper, we use the auxiliary principle technique to prove the existence of a solution of a new class of variational inequalities and to suggest a new novel and general iterative algorithm. We also study the convergence criteria of this algorithm. Several special cases, which can be obtained from our main results, are also discussed.