Abstract and Applied Analysis

Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps

Xiaohong Hu, Zhimiao Fang, and Yunxuan Xiong

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Abstract

The concept of the well posedness for a special scalar problem is linked with strictly efficient solutions of vector optimization problem involving nearly convexlike set-valued maps. Two scalarization theorems and two Lagrange multiplier theorems for strict efficiency in vector optimization involving nearly convexlike set-valued maps are established. A dual is proposed and duality results are obtained in terms of strictly efficient solutions. A new type of saddle point, called strict saddle point, of an appropriate set-valued Lagrange map is introduced and is used to characterize strict efficiency.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2012), Article ID 570918, 9 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450464

Digital Object Identifier
doi:10.1155/2013/570918

Mathematical Reviews number (MathSciNet)
MR3045081

Zentralblatt MATH identifier
1278.90358

Citation

Hu, Xiaohong; Fang, Zhimiao; Xiong, Yunxuan. Strict Efficiency in Vector Optimization with Nearly Convexlike Set-Valued Maps. Abstr. Appl. Anal. 2013, Special Issue (2012), Article ID 570918, 9 pages. doi:10.1155/2013/570918. https://projecteuclid.org/euclid.aaa/1393450464


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