Subdifferential Calculus for Set-Valued Mappings and Optimality Conditions for Multiobjective Optimization Problems
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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.
KeywordsSet-valued vector optimization Subdifferential Optimality conditions Lagrange/Karush/Kuhn/Tucker multipliers
Mathematics Subject Classification90C29 90C26 90C46
The author thanks the anonymous referee and the Editor Hedy Attouch for their helpful remarks that allowed us to improve the original presentation.