CODERIVATIVE CALCULATION RELATED TO A PARAMETRIC AFFINE VARIATIONAL INEQUALITY PART 1: BASIC CALCULATIONS
J.-C. YAO, N. D. YEN
Abstract
Consider a parametric affine variational inequality ; denoted by AVI; for which the pair describes the linear perturbations. Here the matrices and are the given data, is a polyhedral convex constraint set, and denotes the normal cone to at . We study the normal coderivative of the normal-cone operator . In the second part of this paper [20], combining the obtained results with some theorems from Mordukhovich [11], Levy and Mordukhovich [10], Yen and Yao [21], we get sufficient conditions for the Aubin property (the Lipschitz-like property) and the local metric regularity in Robinson’s sense of the solution map of the problem AVI and of the solution map of the problem where is a given vector function. Our investigation complements the well-known work of Dontchev and Rockafellar [3] where the Aubin property of the solution maps and ( is fixed) was established via a critical face condition.