# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2019089

## Optimality conditions for $E$-differentiable vector optimization problems with the multiple interval-valued objective function

 1 Faculty of Mathematics and Computer Science University of Łódź, Banacha 22, 90-238 Łódź, Poland 2 Department of Mathematics, Hadhramout University, P.O. BOX : (50511-50512), Al-Mahrah, Yemen

* Corresponding author: Najeeb Abdulaleem

Received  July 2018 Revised  March 2019 Published  July 2019

In this paper, a nonconvex vector optimization problem with multiple interval-valued objective function and both inequality and equality constraints is considered. The functions constituting it are not necessarily differentiable, but they are $E$-differentiable. The so-called $E$-Karush-Kuhn-Tucker necessary optimality conditions are established for the considered $E$-differentiable vector optimization problem with the multiple interval-valued objective function. Also the sufficient optimality conditions are derived for such interval-valued vector optimization problems under appropriate (generalized) $E$-convexity hypotheses.

Citation: Tadeusz Antczak, Najeeb Abdulaleem. Optimality conditions for $E$-differentiable vector optimization problems with the multiple interval-valued objective function. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2019089
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