Characterization of the Nonemptiness and Weak Compactness of Solution Sets of Nonconvex Vector Optimization Problems

2012 ◽  
Vol 14 (4) ◽  
pp. 346
Author(s):  
Liufen LI
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Weak Compactness ◽  
Vector Optimization Problems ◽  
Solution Sets ◽  
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 Set optimization using improvement sets

2017 ◽  
Vol 27 (2) ◽  
pp. 153-167 ◽  
Author(s):  
M. Dhingra ◽  
C.S. Lalitha
Keyword(s):  
Vector Optimization ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Existence Theorems ◽  
Minimal Solution ◽  
Set Optimization ◽  
Vector Optimization Problems ◽  
Optimal Solutions ◽  
Solution Sets ◽  
Improvement Sets

In this paper we introduce a notion of minimal solutions for set-valued optimization problem in terms of improvement sets, by unifying a solution notion, introduced by Kuroiwa [15] for set-valued problems, and a notion of optimal solutions in terms of improvement sets, introduced by Chicco et al. [4] for vector optimization problems. We provide existence theorems for these solutions, and establish lower convergence of the minimal solution sets in the sense of Painlev?-Kuratowski.

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