Higher-order optimality conditions for strict and weak efficient solutions in set-valued optimization

Higher-order optimality conditions for strict and weak efficient solutions in set-valued optimization

In this paper, we introduce a notion of higher-order Studniarski epiderivative of a set-valued map and study its properties. Then, we discuss their applications to optimality conditions in set-valued optimization. Higher-order optimality conditions for strict and weak efficient solutions of a constr...

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Veröffentlicht in:Positivity : an international journal devoted to the theory and applications of positivity in analysis 2016-06, Vol.20 (2), p.499-514
1. Verfasser: Anh, Nguyen Le Hoang
Format: Artikel
Sprache:eng
Schlagworte:
Calculus of Variations and Optimal Control
Optimization
Econometrics
Fourier Analysis
Mathematics
Mathematics and Statistics
Operator Theory
Optimization
Potential Theory
Studies
System theory
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Zusammenfassung:In this paper, we introduce a notion of higher-order Studniarski epiderivative of a set-valued map and study its properties. Then, we discuss their applications to optimality conditions in set-valued optimization. Higher-order optimality conditions for strict and weak efficient solutions of a constrained set-valued optimization problem are established. Some remarks on the existing results in the literature are given from our results.
ISSN:1385-1292
1572-9281
DOI:10.1007/s11117-015-0369-x