## Abstract and Applied Analysis

### Necessary and Sufficient Conditions for Set-Valued Maps with Set Optimization

#### Abstract

Optimality conditions are studied for set-valued maps with set optimization. Necessary conditions are given in terms of $S$-derivative and contingent derivative. Sufficient conditions for the existence of solutions are shown for set-valued maps under generalized quasiconvexity assumptions.

#### Article information

Source
Abstr. Appl. Anal., Volume 2018 (2018), Article ID 5962049, 6 pages.

Dates
Accepted: 10 December 2017
First available in Project Euclid: 14 February 2018

https://projecteuclid.org/euclid.aaa/1518577260

Digital Object Identifier
doi:10.1155/2018/5962049

Mathematical Reviews number (MathSciNet)
MR3745610

Zentralblatt MATH identifier
06929591

#### Citation

Oussarhan, Abdessamad; Daidai, Ikram. Necessary and Sufficient Conditions for Set-Valued Maps with Set Optimization. Abstr. Appl. Anal. 2018 (2018), Article ID 5962049, 6 pages. doi:10.1155/2018/5962049. https://projecteuclid.org/euclid.aaa/1518577260

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