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Henig Vectorial Proper Efficiency in Real Linear Space and Its Scalarizations

Author: FanZuo
Tutor: QiuJingHui
School: Suzhou University
Course: Basic mathematics
Keywords: real linear spaces Henig proper efficiency scalarization Lagrange multiplier theorem
CLC: O177.3
Type: Master's thesis
Year: 2009
Downloads: 13
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Abstract


In the framework of real linear spaces,we introduce three kinds of Henig proper efficient points.By using the Hahn-Banach separation theorem on convex sets in real linear spaces,we establish the scalarization theorems of the three kinds of Henig proper efficient points respectively.From this,we obtain the scalarizations on Henig proper efficient solutions of vector optimization problems involving nearly cone-subconvexlike vector-vaiued maps and set-valued maps respectively.Moreover,by using the Hahn-Banach separation theorem on product spaces,we give Lagrange multiplier theorems on Henig proper efficient solutions of vector optimization problems involving vector-valued maps and set-valued set maps with constraint.Many known results have been extended to real linear spaces.A new concept of Henig proper efficiency,only involving relatively algebric interior,is introduced and its scalarization is obtained.

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Functional Analysis > The theory of the linear space ( vector space )
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