External and internal stability in set optimization using gamma convergence

2019 ◽  
Vol 35 (3) ◽  
pp. 393-406
Author(s):  
C. S. LALITHA ◽  
◽  
Keyword(s):  
Optimization Problems ◽  
Image Space ◽  
Set Optimization ◽  
Internal Stability ◽  
Gamma Convergence ◽  
Decision Space ◽  
Solution Sets ◽  
Stability Of Solution ◽  
Kuratowski Convergence ◽  
The Stability

The main objective of this paper is to investigate the stability of solution sets of perturbed set optimization problems in the decision space as well as in the image space, by perturbing the objective maps. For a sequence of set-valued maps, a notion of gamma convergence is introduced to establish the external and internal stability in terms of Painlev´e–Kuratowski convergence of sequence of solution sets of perturbed problems under certain compactness assumptions and domination properties.

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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