Optimality conditions based on the Fréchet second-order subdifferential

This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is C 2 -smooth, we show that strengthened second-order necessary optimality conditions are valid if the const...

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Vydáno v:Journal of global optimization Ročník 81; číslo 2; s. 351 - 365
Hlavní autoři: An, D. T. V., Yen, N. D.
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York Springer US 01.10.2021
Springer
Springer Nature B.V
Témata:
Banach spaces
Computer Science
Constraints
Hypotheses
Mathematical functions
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
Second-order tangent set
90C20
90C30
49J53
90C46
Fréchet second-order subdifferential
Second-order necessary optimality conditions
Generalized polyhedral convex set
49K27
Constrained optimization problems on Banach spaces
ISSN:0925-5001, 1573-2916
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Popis
Shrnutí:This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical setting, where the objective function is C 2 -smooth, we show that strengthened second-order necessary optimality conditions are valid if the constraint set is generalized polyhedral convex. For problems in a new setting, where the objective function is just assumed to be C 1 -smooth and the constraint set is generalized polyhedral convex, we establish sharp second-order necessary optimality conditions based on the Fréchet second-order subdifferential of the objective function and the second-order tangent set to the constraint set. Three examples are given to show that the used hypotheses are essential for the new theorems. Our second-order necessary optimality conditions refine and extend several existing results.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-021-01011-4