scholarly journals Linear fractional vector optimization problems with many components in the solution sets

2005 ◽  
Vol 1 (4) ◽  
pp. 477-486 ◽  
Author(s):  
Tran Ninh Hoa ◽  
◽  
Ta Duy Phuong ◽  
Nguyen Dong Yen ◽  
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problems ◽  
Solution Sets

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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