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

Published online by Cambridge University Press:  17 April 2009

Yihong Xu  and
Chuanxi Zhu
Yihong Xu
Affiliation:
Department of Mathematics, Nanchang University, Nanchang, Jiangxi 330047, People's Republic of China, e-mail: xyhxy3946@sina.com
Chuanxi Zhu
Affiliation:
Department of Mathematics, Nanchang University, Nanchang, Jiangxi 330047, People's Republic of China, e-mail: xyhxy3946@sina.com
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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.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 2 , April 2005 , pp. 183 - 192
Copyright
Copyright © Australian Mathematical Society 2005

References

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