Strict Efficiency in Set Optimization Studied with the Set Approach

This paper is devoted to strict efficiency in set optimization studied with the set approach. Strict efficient solutions are defined with respect to the l -type less order relation and the possibly less order relation. Scalar characterization and necessary and/or sufficient conditions for such solut...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 205; no. 2; p. 21
Main Author: Ha, Truong Xuan Duc
Format: Journal Article
Language:English
Published: New York Springer US 01.05.2025
Springer Nature B.V
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control; Optimization
Efficiency
Engineering
Euclidean space
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
Strict efficient solution
Directional derivative
49J53
90C46
Subdifferential
Coderivative
Optimality condition
90C29
Set-valued map
Set optimization
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:This paper is devoted to strict efficiency in set optimization studied with the set approach. Strict efficient solutions are defined with respect to the l -type less order relation and the possibly less order relation. Scalar characterization and necessary and/or sufficient conditions for such solutions are obtained. In particular, we establish some conditions expressed in terms of a high-order directional derivative of set-valued maps and the (convex or limiting) subdifferentials, normal cones and coderivatives. Various illustrating examples are presented.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-025-02617-4