## Taiwanese Journal of Mathematics

- Taiwanese J. Math.
- Advance publication (2019), 14 pages.

### 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

#### Abstract

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

**Source**

Taiwanese J. Math., Advance publication (2019), 14 pages.

**Dates**

First available in Project Euclid: 10 July 2019

**Permanent link to this document**

https://projecteuclid.org/euclid.twjm/1562724021

**Digital Object Identifier**

doi:10.11650/tjm/190604

**Subjects**

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

**Keywords**

set-valued optimization partial order directional derivative optimality conditions

#### Citation

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