Variational Analysis in Semi-Infinite and Infinite Programming, I: Stability of Linear Inequality Systems of Feasible Solutions

This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to parametric problems of semi-infinite and infinite programming, where decision variables run over finite-dimensional and infinite-dimensional spaces, respectively. Part I is primarily de...

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Bibliographic Details
Published in:SIAM journal on optimization Vol. 20; no. 3; pp. 1504 - 1526
Main Authors: Cánovas, M. J., López, M. A., Mordukhovich, B. S., Parra, J.
Format: Journal Article
Language:English
Published: Philadelphia Society for Industrial and Applied Mathematics 01.01.2009
Subjects:
Inequalities
Linear programming
Mathematical analysis
Mathematical models
Norms
Optimization techniques
Perturbation methods
Programming
Stability
Studies
ISSN:1052-6234, 1095-7189
Online Access:Get full text
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Summary:This paper concerns applications of advanced techniques of variational analysis and generalized differentiation to parametric problems of semi-infinite and infinite programming, where decision variables run over finite-dimensional and infinite-dimensional spaces, respectively. Part I is primarily devoted to the study of robust Lipschitzian stability of feasible solutions maps for such problems described by parameterized systems of infinitely many linear inequalities in Banach spaces of decision variables indexed by an arbitrary set T. The parameter space of admissible perturbations under consideration is formed by all bounded functions on T equipped with the standard supremum norm. Unless the index set T is finite, this space is intrinsically infinite-dimensional (nonreflexive and nonseparable) of the ... type. By using advanced tools of variational analysis and exploiting specific features of linear infinite systems, we establish complete characterizations of robust Lipschitzian stability entirely via their initial data with computing the exact bound of Lipschitzian moduli. (ProQuest: ... denotes formulae/symbols omitted.)
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ISSN:1052-6234
1095-7189
DOI:10.1137/090765948