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., Advance publication (2019), 14 pages.

First available in Project Euclid: 10 July 2019

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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., advance publication, 10 July 2019. doi:10.11650/tjm/190604. https://projecteuclid.org/euclid.twjm/1562724021

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