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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Vydané v:Journal of global optimization Ročník 81; číslo 2; s. 351 - 365
Hlavní autori: An, D. T. V., Yen, N. D.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.10.2021
Springer
Springer Nature B.V
Predmet:
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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Abstract 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.
AbstractList 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 [Formula omitted]-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 [Formula omitted]-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.
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 C2-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 C1-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.
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.
Audience Academic
Author An, D. T. V.
Yen, N. D.
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  givenname: N. D.
  surname: Yen
  fullname: Yen, N. D.
  organization: Institute of Mathematics, Vietnam Academy of Science and Technology
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crossref_primary_10_1007_s10957_021_01967_z
crossref_primary_10_1080_00036811_2025_2479060
crossref_primary_10_1007_s10255_025_0028_3
crossref_primary_10_1137_22M1512454
crossref_primary_10_1007_s11590_022_01956_9
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Issue 2
Keywords 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
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PublicationSubtitle An International Journal Dealing with Theoretical and Computational Aspects of Seeking Global Optima and Their Applications in Science, Management and Engineering
PublicationTitle Journal of global optimization
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PublicationYear 2021
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Snippet This paper focuses on second-order necessary optimality conditions for constrained optimization problems on Banach spaces. For problems in the classical...
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SubjectTerms Banach spaces
Computer Science
Constraints
Hypotheses
Mathematical functions
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Real Functions
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Title Optimality conditions based on the Fréchet second-order subdifferential
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