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Lipschitz modulus in convex semi-infinite optimization via d.c.functions

Published online by Cambridge University Press:  19 July 2008

María J. Cánovas ,
Abderrahim Hantoute ,
Marco A. López  and
Juan Parra
María J. Cánovas
Affiliation:
Operations Research Center, Miguel Hernández University of Elche, 03202 Elche, Alicante, Spain. canovas@umh.es; parra@umh.es
Abderrahim Hantoute
Affiliation:
Postdoc researcher at Operations Research Center, Miguel Hernández University of Elche, 03202 Elche, Alicante, Spain. hantoute@ua.es
Marco A. López
Affiliation:
Department of Statistics and Operations Research, University of Alicante, 03071 Alicante, Spain. marco.antonio@ua.es
Juan Parra
Affiliation:
Operations Research Center, Miguel Hernández University of Elche, 03202 Elche, Alicante, Spain. canovas@umh.es; parra@umh.es
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Abstract

We are concerned with the Lipschitz modulus of the optimal set mappingassociated with canonically perturbed convex semi-infinite optimizationproblems. Specifically, the paper provides a lower and an upper bound forthis modulus, both of them given exclusively in terms of the problem's data.Moreover, the upper bound is shown to be the exact modulus when the numberof constraints is finite. In the particular case of linear problems theupper bound (or exact modulus) adopts a notably simplified expression. Ourapproach is based on variational techniques applied to certain difference ofconvex functions related to the model. Some results of [M.J. Cánovas et al., J. Optim. Theory Appl. (2008) Online First](which go back to [M.J. Cánovas, J. Global Optim.41 (2008) 1–13] and [Ioffe, Math. Surveys55 (2000) 501–558; Control Cybern.32 (2003) 543–554])constitute the starting point of the present work.

Keywords

Convex semi-infinite programmingmodulus ofmetric regularityd.c. functions

Information

Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 15 , Issue 4 , October 2009 , pp. 763 - 781
Copyright
© EDP Sciences, SMAI, 2008

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