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Erschienen in:
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2015 | OriginalPaper | Buchkapitel

Estimates of Error Bounds for Some Sets of Efficient Solutions of a Set-Valued Optimization Problem

verfasst von : Truong Xuan Duc Ha

Erschienen in: Set Optimization and Applications - The State of the Art

Verlag: Springer Berlin Heidelberg

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Abstract

In this paper, we establish some estimates of the global/local error bounds for the sets \(S^{\mathrm{Pareto}}_{\bar{y}}\), \(S^{\mathrm{W}}_{\le \bar{y}}\) and \(S^{\mathrm{W}}\), where \(S^{\mathrm{Pareto}}_{\bar{y}}\) is the set of efficient solutions of a unconstrained set-valued optimization problem (\(\mathcal {SP}\)) corresponding to an efficient value \(\bar{y}\) of a unconstrained set-valued optimization problem (\(\mathcal {SP}\)), \(S^{\mathrm{W}}_{\le \bar{y}}\) is the set of weakly efficient solutions of (\(\mathcal {SP}\)) corresponding to weakly efficient values smaller than a weakly efficient value \(\bar{y}\) and \(S^{\mathrm{W}}\) is the set of all weakly efficient solutions of (\(\mathcal {SP}\)). These estimates are expressed in terms of the approximate coderivative, the limiting Fréchet/basic coderivatives and the coderivative of convex analysis. Thus, we establish conditions ensuring the existence of weak sharp minima for (\(\mathcal {SP}\)). We also extend the concept of the good asymptotic behavior to a convex or cone-convex set-valued map.

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Vorheriges Kapitel Set Optimization Meets Variational Inequalities
Nächstes Kapitel On Supremal and Maximal Sets with Respect to Random Partial Orders
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Metadaten
Titel
Estimates of Error Bounds for Some Sets of Efficient Solutions of a Set-Valued Optimization Problem
verfasst von
Truong Xuan Duc Ha
Copyright-Jahr
2015
Verlag
Springer Berlin Heidelberg
Buch
Set Optimization and Applications - The State of the Art

Print ISBN: 978-3-662-48668-9

Electronic ISBN: 978-3-662-48670-2

Copyright-Jahr: 2015

DOI
https://doi.org/10.1007/978-3-662-48670-2_8