## Taiwanese Journal of Mathematics

### $E$-PROPER SADDLE POINTS AND $E$-PROPER DUALITY IN VECTOR OPTIMIZATION WITH SET-VALUED MAPS

#### Abstract

In this paper, based on a kind of unified proper efficiency named as $E$-Benson proper efficiency, we present $E$-proper saddle points theorems and $E$-proper duality results including as weak duality and strong duality theorems of vector optimization problems with set-valued maps. Our main results unify and extend the cases of proper saddle points and proper duality as well as $\varepsilon$-proper saddle points and $\varepsilon$-proper duality.

#### Article information

Source
Taiwanese J. Math., Volume 18, Number 2 (2014), 483-495.

Dates
First available in Project Euclid: 10 July 2017

https://projecteuclid.org/euclid.twjm/1499706399

Digital Object Identifier
doi:10.11650/tjm.18.2014.3473

Mathematical Reviews number (MathSciNet)
MR3188516

Zentralblatt MATH identifier
1357.90148

#### Citation

Zhao, Ke-Quan; Yang, Xin-Min. $E$-PROPER SADDLE POINTS AND $E$-PROPER DUALITY IN VECTOR OPTIMIZATION WITH SET-VALUED MAPS. Taiwanese J. Math. 18 (2014), no. 2, 483--495. doi:10.11650/tjm.18.2014.3473. https://projecteuclid.org/euclid.twjm/1499706399

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