scholarly journals $B$-SEMIPREINVEX FUNCTIONS AND VECTOR OPTIMIZATION PROBLEMS IN BANACH SPACES

2007 ◽  
Vol 11 (3) ◽  
pp. 595-609 ◽  
Author(s):  
Sheng-Lan Chen ◽  
Nan-Jing Huang ◽  
Mu-Ming Wong
Keyword(s):  
Banach Spaces ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Vector Optimization Problems ◽  
Semipreinvex Functions

scholarly journals To the question of regularization of vector optimization problems

2021 ◽  
Vol 16 ◽  
pp. 99
Author(s):  
P.I. Kogut ◽  
I.V. Nechai
Keyword(s):  
Banach Spaces ◽  
Vector Optimization ◽  
Optimization Problems ◽  
Lower Semicontinuous ◽  
Sufficient Conditions ◽  
Vector Optimization Problems ◽  
Method Of Regularization ◽  
Vector Valued

We propose the method of regularization of one class of vector optimizations problems in Banach spaces, in case where vector-valued mapping is not lower semicontinuous in certain sense, which implies violation of sufficient conditions of solvability.

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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