New Optimization Methods for Variational Inequalities and the Computation of Economic Equilibria

Jean-Philippe Vial
LOGILAB-HEC, University of Geneva
JPVial@uni2a.unige.ch

Abstract

Optimization on continuous spaces experienced very substantial changes in the recent years. The new interior point methods allow to tackle problems of considerable size with a remarkably low number of iterations and surprizing efficiency. The methods were originally designed for linear programming; they have been extended to general convex programming, linear and non-linear complementarity problems and variational inequalities. The latter can be approached either by a direct method using the derivatives of the application, or by a cutting plane method on the gap function. We have developed a very robust and efficient cutting plane method based on interior point methods and concepts. We shall present the method and show some typical numerical results on a variety of examples. We shall discuss how to use it on variational inequalities.