Characterization of the Benson Proper Efficiency and Scalarization in Nonconvex Vector Optimization

2001 ◽  
pp. 189-198 ◽  
Author(s):  
Rafail N. Gasimov
Keyword(s):  
Vector Optimization ◽  
Proper Efficiency ◽  
Benson Proper Efficiency ◽  
Nonconvex Vector Optimization

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.

Characterizations of Hartley Proper Efficiency in Nonconvex Vector Optimization

2005 ◽  
Vol 33 (2) ◽  
pp. 273-298 ◽  
Author(s):  
Gue Myung Lee ◽  
Do Sang Kim ◽  
Pham Huu Sach
Keyword(s):  
Vector Optimization ◽  
Proper Efficiency ◽  
Nonconvex Vector Optimization
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