Convex sets and locally convex spaces

2003 ◽  
pp. 31-125
Author(s):  
Nicolas Bourbaki
Keyword(s):  
Convex Sets ◽  
Locally Convex Spaces ◽  
Locally Convex ◽  
Convex Spaces

scholarly journals On super efficiency in set-valued optimisation in locally convex spaces

2005 ◽  
Vol 71 (2) ◽  
pp. 183-192 ◽  
Author(s):  
Yihong Xu ◽  
Chuanxi Zhu
Keyword(s):  
Convex Sets ◽  
Necessary Conditions ◽  
Sufficient Conditions ◽  
Efficient Solutions ◽  
Separation Theorem ◽  
Topological Spaces ◽  
Locally Convex Spaces ◽  
Super Efficiency ◽  
Locally Convex ◽  
Convex Spaces

The set-valued optimisation problem with constraints is considered in the sense of super efficiency in locally convex linear topological spaces. Under the assumption of nearly cone-subconvexlikeness, by applying the separation theorem for convex sets, Kuhn-Tucker and Lagrange necessary conditions for the set-valued optimisation problem to attain its super efficient solutions are obtained. Also, Kuhn-Tucker and Lagrange sufficient conditions are derived. Finally two kinds of unconstrained programs equivalent to set-valued optimisation problems are established.

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