Strict Efficiency in Set Optimization Studied with the Set Approach

Truong Xuan Duc Ha ()
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Truong Xuan Duc Ha: Thanglong University

Journal of Optimization Theory and Applications, 2025, vol. 205, issue 2, No 2, 20 pages

Abstract: Abstract 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.

Keywords: Set optimization; Strict efficient solution; Optimality condition; Directional derivative; Subdifferential; Coderivative; Set-valued map; 49J53; 90C29; 90C46 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-025-02617-4

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