Unified optimality conditions for set-valued optimizations

Geng-Hua Li; Sheng-Jie Li

doi:10.3934/jimo.2018087

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2019, Volume 15, Issue 3: 1101-1116. Doi: 10.3934/jimo.2018087

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Unified optimality conditions for set-valued optimizations

Geng-Hua Li and
Sheng-Jie Li^,

College of Mathematics and Statistics, Chongqing University, Chongqing, 401331, China

* Corresponding author: Sheng-Jie Li
* Corresponding author: Sheng-Jie Li

Received: June 30, 2016

Revised: April 30, 2017

Early access: June 2018

Published: April 2019

This research was supported by the National Natural Science Foundation of China (Grant numbers: 11171362, 11571055).

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Abstract

This paper is devoted to the study of unified optimality conditions for constrained set-valued optimization problems via image space analysis. Necessary and sufficient optimality conditions are given in terms of tangent cones of extended image set. By exploiting such results, we analyse the optimality conditions employing different generalized derivatives.

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Mathematics Subject Classification: Primary: 90C31, 90C46; Secondary: 49J53.

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