scholarly journals A Characterization ofE-Benson Proper Efficiency via Nonlinear Scalarization in Vector Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Ke Quan Zhao ◽  
Yuan Mei Xia ◽  
Hui Guo
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Proper Efficiency ◽  
Vector Optimization Problems ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Benson Proper Efficiency ◽  
Scalarization Function

A class of vector optimization problems is considered and a characterization ofE-Benson proper efficiency is obtained by using a nonlinear scalarization function proposed by Göpfert et al. Some examples are given to illustrate the main results.

scholarly journals A Kind of Unified Proper Efficiency in Vector Optimization

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Ke Quan Zhao ◽  
Yuan Mei Xia
Keyword(s):  
Vector Optimization ◽  
Proper Efficiency ◽  
Nonlinear Scalarization ◽  
Benson Proper Efficiency

Based on the ideas of the classical Benson proper efficiency, a new kind of unified proper efficiency namedS-Benson proper efficiency is introduced by using Assumption (B) proposed by Flores-Bazán and Hernández, which unifies some known exact and approximate proper efficiency including(C,ε)-proper efficiency andE-Benson proper efficiency in vector optimization. Furthermore, a characterization ofS-Benson proper efficiency is established via a kind of nonlinear scalarization functions introduced by Göpfert et al.

scholarly journals Weak Sharp Minima in Set-Valued Optimization Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-9
Author(s):  
Ming-hao Jin ◽  
Jun-xiang Wang ◽  
Shu Xu
Keyword(s):  
Necessary Conditions ◽  
Optimization Problems ◽  
Nonlinear Scalarization Function ◽  
Nonlinear Scalarization ◽  
Outer Limit ◽  
Sufficient And Necessary Conditions ◽  
Scalarization Function ◽  
Weak Sharp ◽  
Sharp Minima

We introduce the notion of a weakψ-sharp minimizer for set-valued optimization problems. We present some sufficient and necessary conditions that a pair point is a weakψ-sharp minimizer through the outer limit of set-valued map and develop the characterization of the weakψ-sharp minimizer in terms of a generalized nonlinear scalarization function. These results extend the corresponding ones in Studniarski (2007).

Sign in / Sign up

Export Citation Format

Share Document