Strict feasibility and solvability for vector equilibrium problems in reflexive Banach spaces

2010 ◽  
Vol 5 (3) ◽  
pp. 505-514 ◽  
Author(s):  
Rong Hu ◽  
Ya Ping Fang
Keyword(s):  
Banach Spaces ◽  
Equilibrium Problems ◽  
Vector Equilibrium Problems ◽  
Reflexive Banach Spaces ◽  
Strict Feasibility ◽  
Vector Equilibrium

scholarly journals Sharp Efficiency for Vector Equilibrium Problems on Banach Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Si-Huan Li ◽  
Qiang Wang ◽  
Shu Xu ◽  
Jun-Xiang Wang
Keyword(s):  
Optimality Conditions ◽  
Banach Spaces ◽  
Normal Cone ◽  
Equilibrium Problems ◽  
Necessary Optimality Conditions ◽  
Efficient Solutions ◽  
Vector Optimization Problem ◽  
Sufficient Optimality Conditions ◽  
Vector Equilibrium Problems ◽  
Vector Equilibrium

The concept of sharp efficient solution for vector equilibrium problems on Banach spaces is proposed. Moreover, the Fermat rules for local efficient solutions of vector equilibrium problems are extended to the sharp efficient solutions by means of the Clarke generalized differentiation and the normal cone. As applications, some necessary optimality conditions and sufficient optimality conditions for local sharp efficient solutions of a vector optimization problem with an abstract constraint and a vector variational inequality are obtained, respectively.

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