Second-Order Analysis of Polyhedral Systems in Finite and Infinite Dimensions with Applications to Robust Stability of Variation

Abstract. This paper concerns second-order analysis for a remarkable class of variational systems in finite-dimensional and infinite-dimensional spaces, which is particularly important for the study of optimization and equilibrium problems with equilibrium constraints. Systems of this type are described via variational inequalities over polyhedral convex sets and allow us to provide a comprehensive local analysis by using appropriate generalized differentiation of the normal cone mappings for such sets. In this paper we efficiently compute the required coderivatives of the normal cone mappings exclusively via the initial data of polyhedral sets in reflexive Banach spaces. This provides the main tools of second-order variational analysis allowing us, in particular, to derive necessary and sufficient conditions for robust Lipschitzian stability of solution maps to parameterized variational inequalities with evaluating the exact bound of the corresponding Lipschitzian moduli. The effi...

• Type: Journal
• Year: 2010
• Where: SIAMJO
• Authors: René Henrion, Boris S. Mordukhovich, Nguyen Mau Nam
• Keywords: Normal Cone Mappings, SIAMJO 2010, Variational, Variational Inequalities