Uniqueness for Quasi-variational Inequalities

作者：Dreves Axel^*

来源：Set-Valued and Variational Analysis, 2016, 24(2): 285-297.

DOI：10.1007/s11228-015-0339-2

• Quasi-variational inequalities
• Uniqueness
• Continuation approach
• Implicit function

This paper presents a uniqueness result for a quasi-variational inequality QVI(1) 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 QVI(0), 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 QVI(0) to a solution of QVI(1). Finally, we can show that the existence of a second different solution of QVI(1) contradicts the nonsingularity condition. Moreover, we present some matrix-based 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.

• 出版日期2016-6