$E$-super efficiency of set-valued optimization problems involving improvement sets

Zhiang  Zhou; Xinmin Yang; Kequan  Zhao

doi:10.3934/jimo.2016.12.1031

Article Contents

2016, Volume 12, Issue 3: 1031-1039. Doi: 10.3934/jimo.2016.12.1031

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$E$-super efficiency of set-valued optimization problems involving improvement sets

1.
College of Mathematics and Statistics, Chongqing University of Technology, Chongqing 400054
2.
Department of Mathematics, Chongqing Normal University, Chongqing 400047
3.
College of Mathematics Science, Chongqing normal University, Chongqing 400047

Received: October 31, 2014

Revised: April 30, 2015

Published: June 2016

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Abstract

In this paper, $E$-super efficiency of set-valued optimization problems is investigated. Firstly, based on the improvement set, a new notion of $E$-super efficient point is introduced in real locally convex spaces. Secondly, under the assumption of near $E$-subconvexlikeness of set-valued maps, scalarization theorems of set-valued optimization problems are established in the sense of $E$-super efficiency. Finally, Lagrange multiplier theorems of set-valued optimization problems are obtained in the sense of $E$-super efficiency.

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Mathematics Subject Classification: 90C26, 90C29, 90C30.

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