Optimality Conditions of the Set-valued Optimization Problem with Generalized Cone Convex Set-valued Maps Characterized by Contingent Epiderivative

In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the conting...

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Published inActa Mathematicae Applicatae Sinica Vol. 34; no. 1; pp. 11 - 18
Main Authors Zhou, Zhi-ang, Yang, Xin-min, Qiu, Qiu-sheng
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2018
Springer Nature B.V
EditionEnglish series
Subjects
Applications of Mathematics
Math Applications in Computer Science
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Optimization
Theoretical
optimality conditions
Henig proper efficiency
90C30
contingent epiderivative
generalized cone convexity
set-valued maps
90C29
90C26
Online AccessGet full text
ISSN0168-9673
1618-3932
DOI10.1007/s10255-018-0727-0

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Summary:In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.
Bibliography:11-2041/O1
In this paper, firstly, a new notion of generalized cone convex set-valued map is introduced in real normed spaces. Secondly, a property of the generalized cone convex set-valued map involving the contingent epiderivative is obtained. Finally, as the applications of this property, we use the contingent epiderivative to establish optimality conditions of the set-valued optimization problem with generalized cone convex set-valued maps in the sense of Henig proper efficiency. The results obtained in this paper generalize and improve some known results in the literature.
set-valued maps; generalized cone convexity; Henig proper efficiency; contingent epiderivative;optimality conditions
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ISSN:0168-9673
1618-3932
DOI:10.1007/s10255-018-0727-0