Subdifferential Calculus for Set-Valued Mappings and Optimality Conditions for Multiobjective Optimization Problems

Ahmed Taa ()
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Ahmed Taa: Faculté des Sciences et Techniques de Marrakech

Journal of Optimization Theory and Applications, 2019, vol. 180, issue 2, No 4, 428-441

Abstract: Abstract In this work, we provide a generalized formula for the weak subdifferential (resp., for the Benson proper subdifferential) of the sum of two cone-closed and cone-convex set-valued mappings, under the Attouch–Brézis qualification condition. This formula is applied to establish necessary and sufficient optimality conditions in terms of Lagrange/Karush/Kuhn/Tucker multipliers for the existence of the weak (resp., of the Benson proper) efficient solutions of a set-valued vector optimization problem.

Keywords: Set-valued vector optimization; Subdifferential; Optimality conditions; Lagrange/Karush/Kuhn/Tucker multipliers; 90C29; 90C26; 90C46 (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s10957-018-1406-2

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