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

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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.

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Acknowledgements

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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  1. Département de Mathématiques, Faculté des Sciences et Techniques de Marrakech, B.P. 549, Marrakech, Morocco

    Ahmed Taa

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  1. Ahmed Taa
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Correspondence to Ahmed Taa.

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Communicated by Hedy Attouch.

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Taa, A. Subdifferential Calculus for Set-Valued Mappings and Optimality Conditions for Multiobjective Optimization Problems. J Optim Theory Appl 180, 428–441 (2019). https://doi.org/10.1007/s10957-018-1406-2

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  • DOI: https://doi.org/10.1007/s10957-018-1406-2

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