Journal of Optimization Theory and Applications

, Volume 180, Issue 2, pp 428–441 | Cite as

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

  • Ahmed TaaEmail author


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.


Set-valued vector optimization Subdifferential Optimality conditions Lagrange/Karush/Kuhn/Tucker multipliers 

Mathematics Subject Classification

90C29 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.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Département de MathématiquesFaculté des Sciences et Techniques de MarrakechMarrakechMorocco

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