Uniqueness for Quasivariational Inequalities

Authors: Axel Dreves

Publish Date: 2015/08/01

Volume: 24, Issue: 2, Pages: 285-297

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Abstract

This paper presents a uniqueness result for a quasivariational inequality QVI1 that in contrast to existing results does not require the projection mapping on a variable closed and convex set to be a contraction Our basic idea is to find a simple QVI0 for example a variational inequality for which we can show the existence of a unique solution Further exploiting some nonsingularity condition we will guarantee the existence of a continuous solution path from the unique solution of QVI0 to a solution of QVI1 Finally we can show that the existence of a second different solution of QVI1 contradicts the nonsingularity condition Moreover we present some matrixbased sufficient conditions for our nonsingularity assumption and we discuss these assumptions in the context of generalized Nash equilibrium problems with quadratic cost and affine linear constraint functions

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