Taiwanese Journal of Mathematics

Optimality Conditions in Set-valued Optimization Problem with Respect to a Partial Order Relation via Directional Derivative

Emrah Karaman, Mustafa Soyertem, and İlknur Atasever Güvenç

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In this study, a new directional derivative is defined by using Minkowski difference. Some properties and existence theorems of this directional derivative are given. Moreover, necessary and sufficient optimality conditions are presented for set-valued optimization problems with respect to $m_1$ order relation via directional derivative.

Article information

Taiwanese J. Math., Volume 24, Number 3 (2020), 709-722.

Received: 30 October 2018
Revised: 22 February 2019
Accepted: 17 June 2019
First available in Project Euclid: 19 May 2020

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Primary: 80M50: Optimization 90C26: Nonconvex programming, global optimization

set-valued optimization partial order directional derivative optimality conditions


Karaman, Emrah; Soyertem, Mustafa; Güvenç, İlknur Atasever. Optimality Conditions in Set-valued Optimization Problem with Respect to a Partial Order Relation via Directional Derivative. Taiwanese J. Math. 24 (2020), no. 3, 709--722. doi:10.11650/tjm/190604. https://projecteuclid.org/euclid.twjm/1589875226

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