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Abstract vector space extremum Optimality conditions and Lagrange Duality

Author: WangChuanTao
Tutor: LiZeMin
School: Chongqing University
Course: Computational Mathematics
Keywords: Alternative theorem Optimality conditions SCALARIZATION Saddle point Duality
CLC: O177.3
Type: Master's thesis
Year: 2007
Downloads: 50
Quote: 2
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This paper discusses the problem of infinite dimensional vector extreme number of issues . In locally convex linear topological space , the use of relative interior , the definition of (v, OY; U) generalized subconvexlike mapping concepts and discuss some of its properties , the establishment of alternative theorem this map . Using this theorem in locally convex linear topological space obtained with generalized inequality constraints Vector Extremum Problems optimality conditions . In order linear space , using the literature [ 62 ] definition of generalized convexity and have come to the alternative theorem obtained generalized linear spaces with inequality constraints Vector Extremum Problems optimality conditions . Linear space in order to obtain a vector-valued optimization problems scalarization results and prove the existence theorem Lagrangian multipliers . Then, in order to introduce the linear space FJ saddle point , KT saddle point , discuss them with inequality constraints with Generalized Vector Extremum Problems relationship between weakly efficient solution . On this basis , given the magnitude of the vector-valued optimization problems Lagrange Duality , including the weak duality theorem, strong duality theorem and converse duality theorems .

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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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