Benson Proper Efficiency in Set-Valued Optimization on Real Linear Spaces

2006 ◽  
pp. 45-59 ◽  
Author(s):  
Elvira Hernández ◽  
Bienvenido Jiménez ◽  
Vicente Novo
Keyword(s):  
Proper Efficiency ◽  
Linear Spaces ◽  
Benson Proper Efficiency ◽  
Real Linear

Characterizations of Benson proper efficiency of set-valued optimization in real linear spaces

2019 ◽  
Vol 17 (1) ◽  
pp. 1168-1182
Author(s):  
Hongwei Liang ◽  
Zhongping Wan
Keyword(s):  
Optimization Problem ◽  
Saddle Points ◽  
Sufficient Conditions ◽  
Proper Efficiency ◽  
Solid Cone ◽  
Linear Spaces ◽  
New Class ◽  
Benson Proper Efficiency ◽  
Real Linear ◽  
Necessary And Sufficient

Abstract A new class of generalized convex set-valued maps termed relatively solid generalized cone-subconvexlike maps is introduced in real linear spaces not equipped with any topology. This class is a generalization of generalized cone-subconvexlike maps and relatively solid cone-subconvexlike maps. Necessary and sufficient conditions for Benson proper efficiency of set-valued optimization problem are established by means of scalarization, Lagrange multipliers, saddle points and duality. The results generalize and improve some corresponding ones in the literature. Some examples are afforded to illustrate our results.

On the Intrinsic Core of Convex Cones in Real Linear Spaces

2021 ◽  
Vol 31 (2) ◽  
pp. 1276-1298
Author(s):  
Bahareh Khazayel ◽  
Ali Farajzadeh ◽  
Christian Günther ◽  
Christiane Tammer
Keyword(s):  
Convex Cones ◽  
Linear Spaces ◽  
Real Linear

scholarly journals Nearly directed subspaces of partially ordered linear spaces

1968 ◽  
Vol 16 (2) ◽  
pp. 135-144
Author(s):  
G. J. O. Jameson
Keyword(s):  
Linear Space ◽  
Transitive Relation ◽  
Linear Spaces ◽  
Real Linear Space ◽  
Partially Ordered ◽  
Real Linear ◽  
Image Position ◽  
Ordered Linear Spaces

Let X be a partially ordered linear space, i.e. a real linear space with a reflexive, transitive relation ≦ such that

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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