Semicontinuity of the Minimal Solution Set Mappings for Parametric Set-Valued Vector Optimization Problems

2019 ◽  
Author(s):  
Xin Xu ◽  
Yang-Dong Xu ◽  
Yue-Ming Sun
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Minimal Solution ◽  
Solution Set ◽  
Vector Optimization Problems ◽  
Set Mappings

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.

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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