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Second-order analysis of polyhedral systems in finite and infinite dimensions with applications to robust stability of variational inequalities

Please always quote using this URN:urn:nbn:de:0296-matheon-5534
  • 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 efficient coderivative calculations and characterizations of robust stability obtained in this paper are the first results in the literature for the problems under consideration in infinite-dimensional spaces. Most of them are also new in finite dimensions.

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Metadaten
Author:Rene Henrion, Boris S. Mordukhovich, Nguyen Mau Nam
URN:urn:nbn:de:0296-matheon-5534
Referee:Fredi Tröltzsch
Document Type:Preprint, Research Center Matheon
Language:English
Date of first Publication:2009/03/02
Release Date:2009/02/02
Tag:
Institute:Humboldt-Universität zu Berlin
Weierstraß-Institut für Angewandte Analysis und Stochastik (WIAS)
MSC-Classification:49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Jxx Existence theories / 49J52 Nonsmooth analysis [See also 46G05, 58C50, 90C56]
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX] / 49Kxx Optimality conditions / 49K40 Sensitivity, stability, well-posedness [See also 90C31]
58-XX GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15) / 58Cxx Calculus on manifolds; nonlinear operators [See also 46Txx, 47Hxx, 47Jxx] / 58C20 Differentiation theory (Gateaux, Fréchet, etc.) [See also 26Exx, 46G05]
Preprint Number:549
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