Second-order optimality conditions for efficiency in C1,1-smooth quasiconvex multiobjective programming problem

This paper deals with a quasiconvex multiobjective programming problem with inequality and set constraints with C 1 , 1 -smooth data. Based on the definition of quasiconvexity, pseudoconvexity and second-order Mordukhovich/Fréchet subdifferentials of extended-real-valued function, we propose the two...

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Veröffentlicht in:Computational & applied mathematics Jg. 40; H. 6
Hauptverfasser: Su, Tran Van, Hang, Dinh Dieu
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Cham Springer International Publishing 01.09.2021
Springer Nature B.V
Schlagworte:
Applications of Mathematics
Applied physics
Computational mathematics
Computational Mathematics and Numerical Analysis
Mathematical Applications in Computer Science
Mathematical Applications in the Physical Sciences
Mathematical functions
Mathematical programming
Mathematics
Mathematics and Statistics
90C46
Smooth quasiconvex multiobjective programming problem with constraints
49J52
Second-order Mordukhovich/Fréchet Subdifferentials
Second-order optimality conditions
90C29
Weak Efficiency
Generalized second-order Ben-Tal constraint qualifications
49K27
ISSN:2238-3603, 1807-0302
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Zusammenfassung:This paper deals with a quasiconvex multiobjective programming problem with inequality and set constraints with C 1 , 1 -smooth data. Based on the definition of quasiconvexity, pseudoconvexity and second-order Mordukhovich/Fréchet subdifferentials of extended-real-valued function, we propose the two generalized Ben-Tal second-order constraint qualifications and then establish strong and weak Karush-Kuhn-Tucker type second-order necessary optimality conditions for weak efficiency to such problem. Under some suitable assumptions on the pseudoconvexity and C 1 , 1 -around a feasible solution of objective and constraint functions, some second-order sufficient optimality conditions in terms of Fréchet subdifferentials are presented. An application of the result on sufficient optimality of order two in terms of Mordukhovich subdifferentials in the sense of the functions belong to C 2 -around a feasible solution is obtained. Some examples are also provided to demonstrate for our findings.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:2238-3603
1807-0302
DOI:10.1007/s40314-021-01625-0