Contingent derivatives and necessary efficiency conditions for vector equilibrium problems with constraints

2018 ◽  
Vol 52 (2) ◽  
pp. 543-559 ◽  
Author(s):  
Do Van Luu ◽  
Tran Van Su
Keyword(s):  
Equilibrium Problems ◽  
Necessary Conditions ◽  
Constraint Qualifications ◽  
Efficient Solutions ◽  
Vector Equilibrium Problems ◽  
Vector Equilibrium ◽  
Efficiency Conditions

We establish Fritz John necessary conditions for local weak efficient solutions of vector equilibrium problems with constraints in terms of contingent derivatives. Under suitable constraint qualifications, Karush–Kuhn–Tucker necessary conditions for those solutions are investigated.

Connectedness of the sets of weak efficient solutions for generalized vector equilibrium problems

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Qing-You Liu ◽  
Xian-Jun Long ◽  
Nan-jing Huang
Keyword(s):  
Equilibrium Problem ◽  
Equilibrium Problems ◽  
Efficient Solutions ◽  
Vector Equilibrium Problem ◽  
Vector Equilibrium Problems ◽  
Generalized Vector Equilibrium Problem ◽  
Generalized Vector Equilibrium Problems ◽  
Vector Equilibrium ◽  
Locally Convex

AbstractIn this paper, a generalized vector equilibrium problem is introduced and studied. A scalar characterization of weak efficient solutions for the generalized vector equilibrium problem is obtained. By using the scalarization result, the existence of the weak efficient solutions and the connectedness of the set of weak efficient solutions for the generalized vector equilibrium problem are proved in locally convex spaces.

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