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Variational Convergence of Bifunctions: Motivating Applications

Alejandro Jofré(ajofre***at***dim.Uchile.cl)
Roger J-B Wets(rjbwets***at***ucdavis.edu)

Abstract: It's shown that a number of variational problems can be cast as finding the maxinf-points (or minsup-points) of bivariate functions, coveniently abbreviated to bifunctions. These variational problems include: linear and nonlinear complementarity problems, fixed points, variational inequalities, inclusions, non-cooperative games, Walras and Nash equilibrium problems. One can then appeal to the theory of lopsided convergence for bifunctions to derive a variety of stability results for each one of these variational problems.

Keywords: lop-convergence, lopsided convergence, maxinf-points, Ky Fan Functions, variational inequalities, Nash and Walras equilibrium points, fixed points, inequality systems, inclusion systems, generalized equations

Category 1: Complementarity and Variational Inequalities

Category 2: Other Topics (Game Theory )

Category 3: Convex and Nonsmooth Optimization (Other )

Citation: Tech. Note, University of California, Davis, December 2010

Download: [PDF]

Entry Submitted: 02/04/2011
Entry Accepted: 02/04/2011
Entry Last Modified: 02/04/2011

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