Duality and saddle-points for convex-like vector optimization problems on real linear spaces

Top ◽  
2005 ◽  
Vol 13 (2) ◽  
pp. 343-357 ◽  
Author(s):  
Miguel Adán ◽  
Vicente Novo
Keyword(s):  
Vector Optimization ◽  
Optimization Problems ◽  
Saddle Points ◽  
Vector Optimization Problems ◽  
Linear Spaces ◽  
Real Linear

scholarly journals ϵ-Henig Saddle Points and Duality of Set-Valued Optimization Problems in Real Linear Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Zhi-Ang Zhou
Keyword(s):  
Saddle Point ◽  
Optimization Problem ◽  
Optimization Problems ◽  
Saddle Points ◽  
Linear Spaces ◽  
Equivalent Characterization ◽  
Generalized Cone Subconvexlikeness ◽  
Real Linear ◽  
The Relationship

We studyϵ-Henig saddle points and duality of set-valued optimization problems in the setting of real linear spaces. Firstly, an equivalent characterization ofϵ-Henig saddle point of the Lagrangian set-valued map is obtained. Secondly, under the assumption of the generalized cone subconvexlikeness of set-valued maps, the relationship between theϵ-Henig saddle point of the Lagrangian set-valued map and theϵ-Henig properly efficient element of the set-valued optimization problem is presented. Finally, some duality theorems are given.

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