Variational Inequalities: Theory & Computation

TB05.1 Implicit Solutions of Parametric Variational Inequalities Danny Ralph --- Univ. of Melbourne, Dept. of Math., Parkville, Victoria, 3052 , Australia (danny@mundoe.maths.mu.oz.au)

We discuss conditions for the existence of locally unique solutions¨ of parametric nonlinear variational inequalities. This builds on¨ Karush-Kuhn-Tucker conditions and a 'strong coherent orientation¨ condition' highlighted in recent work with Luo & Pang, but does not¨ rely on the uniqueness of KKT multipliers. Some motivation for this¨ study is given.

TB05.2 Characterizations of the Local Single-Valuedness of Multifunctions with Applications to Variational Inequalities Rene Poliquin, Adam Levy --- Univ. of Alberta, Dept. of Math., Edmonton, Alberta, , Canada T6G 2G1 (rene@fenchel.math.ualberta.ca)

We characterize the local single-valuedness and continuity of¨ set-valued mappings in terms of their 'premonotonicity' and lower¨ semicontinuity. As an application of our results, we determine when¨ solutions to generalized variational inequalities, e.g., KKT pairs¨ in parametric optimization, are locally unique and Lipschitz¨ continuous.

TB05.3 An Algorithm for Solving Generalized Equations Involving Polyhedral Multifunctions Stephen C. Billups --- Univ. of CO, Dept. of Math., CB 170, PO Box 173364, Denver, CO 80217-3364, (sbillups@carbon.cudenver.edu)

We present an algorithm for solving generalized equations involving¨ polyhedral multifunctions. Most algorithmic work in this area¨ focuses on the special case where the multifunction is the normal¨ cone to a convex set. We solve the more general problem by using a¨ generalization of Robinson's normal map.