An algorithm for minimizing a strongly convex function on the equilibrium set of price equilibrium models

Abstract

We consider a class of equilibrium models including the im plicit Walras supply-demand and competitive models that, in general, is ill posed. We formulate such a model in the form a variational inequality hav ing certain monotonicity property which allows us to describe an algorithm avoiding the ill-posedness by finding the equilibrium point that is nearest to the given guessed or desired equilibrium price for the model. A main difficulty of the problem is that its feasible domain is not given explicitly as in a standard convex programming problem. The proposed algorithm is a combination between the gradient one and the Mann-Krashnoschelskii f ixed point procedure. The obtained computational results with many ran domly generated data show that the proposed algorithm works well for this class of the equilibrium models.