On the Stability of the Solution Set Mappings to Parametric Set Optimization Problems

2015 ◽  
Vol 4 (2) ◽  
pp. 255-263 ◽  
Author(s):  
Yang-Dong Xu ◽  
Ping-Ping Zhang
Keyword(s):  
Optimization Problems ◽  
Solution Set ◽  
Set Optimization ◽  
The Stability ◽  
Set Mappings ◽  
Stability Of The Solution

STABILITY OF THE SOLUTION SET OF NON-COERCIVE VARIATIONAL INEQUALITIES

2002 ◽  
Vol 04 (01) ◽  
pp. 145-160 ◽  
Author(s):  
SAMIR ADLY ◽  
MICHEL THÉRA ◽  
EMIL ERNST
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Convex Analysis ◽  
Convex Sets ◽  
Solution Set ◽  
Small Perturbations ◽  
The Stability ◽  
Stability Of The Solution

In this paper, we study the stability of the solution set of a non-coercive variational inequality with respect to small perturbations of the data involved in the problem. This research is done using well-known tools of convex analysis and the concept of well-positioned convex sets (which is defined and studied).

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.

Qualitative properties of solutions to set optimization problems

2021 ◽  
Vol 40 (2) ◽  
Author(s):  
Lam Quoc Anh ◽  
Nguyen Huu Danh ◽  
Pham Thanh Duoc ◽  
Tran Ngoc Tam
Keyword(s):  
Optimization Problems ◽  
Set Optimization ◽  
Qualitative Properties ◽  
Qualitative Properties Of Solutions

scholarly journals Structure of Pareto Solutions of Generalized Polyhedral-Valued Vector Optimization Problems in Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Qinghai He ◽  
Weili Kong
Keyword(s):  
Banach Spaces ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problem ◽  
Solution Set ◽  
Pareto Optimal ◽  
Pareto Solution ◽  
Value Set ◽  
Set Valued Mapping ◽  
Optimal Value

In general Banach spaces, we consider a vector optimization problem (SVOP) in which the objective is a set-valued mapping whose graph is the union of finitely many polyhedra or the union of finitely many generalized polyhedra. Dropping the compactness assumption, we establish some results on structure of the weak Pareto solution set, Pareto solution set, weak Pareto optimal value set, and Pareto optimal value set of (SVOP) and on connectedness of Pareto solution set and Pareto optimal value set of (SVOP). In particular, we improved and generalize, Arrow, Barankin, and Blackwell’s classical results in Euclidean spaces and Zheng and Yang’s results in general Banach spaces.

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