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

Tadeusz Antczak; Najeeb Abdulaleem

doi:10.3934/jimo.2019089

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2020, Volume 16, Issue 6: 2971-2989. Doi: 10.3934/jimo.2019089

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

Tadeusz Antczak^1, and
Najeeb Abdulaleem^2, ,

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
^* Corresponding author: Najeeb Abdulaleem

Received: July 2018

Revised: March 2019

Early access: July 22, 2019

Published online: July 22, 2019

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Abstract

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.

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Mathematics Subject Classification: Primary: 90C29, 90C30, 90C46, 90C26.

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