Ennouri Tazi, Calculus rules of generalized proper $\epsilon$-subdifferential for vector valued mappings and applications

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DOI: 10.23952/jano.7.2025.2.04
Volume 7, Issue 2, 1 August 2025, Pages 199-213

Abstract. This paper deals with a new concept of subdifferential defined in the Pareto sense and adapted to nonconvex vector mappings, called generalized proper $\epsilon$ -subdifferential. Some existence theorems and properties are discussed. We establish some formulas of the generalized proper $\epsilon$ -subdifferential for the sum and the difference of two vector valued mappings. As an application of the calculus rules, we establish necessary and sufficient optimality conditions for a constrained vector optimization problem with the difference of two vector valued mappings.

How to Cite this Article:
E. Tazi, Calculus rules of generalized proper $\epsilon$ -subdifferential for vector valued mappings and applications, J. Appl. Numer. Optim. 7 (2025), 199-213.