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Sensitivity Analysis of Parameterized Variational Inequalities

School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA
ashapiro{at}isye.gatech.edu

In this paper we discuss local uniqueness, continuity, and differentiability properties of solutions of parameterized variational inequalities (generalized equations). To this end we use two types of techniques. One approach consists in formulating variational inequalities in a form of optimization problem based on regularized gap functions, and applying a general theory of perturbation analysis of parameterized optimization problems. Another approach is based on a theory of contingent (outer graphical) derivatives and some results about differentiability properties of metric projections.

Key Words: variational inequalities; gap functions; sensitivity analysis; second order regularity; quadratic growth condition; locally upper Lipschitz and Hölder continuity; directional differentiability; prox-regularity; graphical derivatives
History: Received: June 7, 2003; revision received: February 9, 2004;