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Titlebook: Convexity and Optimization in Finite Dimensions I; Josef Stoer,Christoph Witzgall Book 1970 Springer-Verlag Berlin · Heidelberg 1970 Arith

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書目名稱Convexity and Optimization in Finite Dimensions I
編輯Josef Stoer,Christoph Witzgall
視頻videohttp://file.papertrans.cn/238/237862/237862.mp4
叢書名稱Grundlehren der mathematischen Wissenschaften
圖書封面Titlebook: Convexity and Optimization in Finite Dimensions I;  Josef Stoer,Christoph Witzgall Book 1970 Springer-Verlag Berlin · Heidelberg 1970 Arith
描述Dantzig‘s development of linear programming into one of the most applicable optimization techniques has spread interest in the algebra of linear inequalities, the geometry of polyhedra, the topology of convex sets, and the analysis of convex functions. It is the goal of this volume to provide a synopsis of these topics, and thereby the theoretical back- ground for the arithmetic of convex optimization to be treated in a sub- sequent volume. The exposition of each chapter is essentially independent, and attempts to reflect a specific style of mathematical reasoning. The emphasis lies on linear and convex duality theory, as initiated by Gale, Kuhn and Tucker, Fenchel, and v. Neumann, because it represents the theoretical development whose impact on modern optimi- zation techniques has been the most pronounced. Chapters 5 and 6 are devoted to two characteristic aspects of duality theory: conjugate functions or polarity on the one hand, and saddle points on the other. The Farkas lemma on linear inequalities and its generalizations, Motzkin‘s description of polyhedra, Minkowski‘s supporting plane theorem are indispensable elementary tools which are contained in chapters 1, 2 and 3, resp
出版日期Book 1970
關鍵詞Arithmetic; Convexity; Dimensions; Finite; Konvexe Planungsrechnung; Topology; algebra; function; geometry; t
版次1
doihttps://doi.org/10.1007/978-3-642-46216-0
isbn_softcover978-3-642-46218-4
isbn_ebook978-3-642-46216-0Series ISSN 0072-7830 Series E-ISSN 2196-9701
issn_series 0072-7830
copyrightSpringer-Verlag Berlin · Heidelberg 1970
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書目名稱Convexity and Optimization in Finite Dimensions I影響因子(影響力)




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Convex Sets,le point theorems. The material presented is mostly classical: The important separation theorems for convex sets, the existence of supports, Helly’s theorem, and Brouwer’s fixed point theorem (see Bonnesen and Fenchel [.], Eggleston [.], and Fan [.]). In addition, extreme sets are discussed in detai
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Saddle Point Theorems,ept has been found to apply in a much larger context. It is also a natural and rich source for duality theorems. In fact, every theorem stating the existence of a “saddle point” can be interpreted as duality theorem for a pair of dual programs.
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Managing Composite Web ServicesIt uses the oldest and most straightforward approach. There is no concern for geometrical interpretations or arithmetical efficiency as in other chapters. The systems are viewed as sets of relations, either true or false, and their logical structure and interdependence is investigated.
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Application Management and Web Servicesle point theorems. The material presented is mostly classical: The important separation theorems for convex sets, the existence of supports, Helly’s theorem, and Brouwer’s fixed point theorem (see Bonnesen and Fenchel [.], Eggleston [.], and Fan [.]). In addition, extreme sets are discussed in detail.
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發(fā)表于 2025-3-22 21:39:57 | 只看該作者
Managing Composite Web Servicesept has been found to apply in a much larger context. It is also a natural and rich source for duality theorems. In fact, every theorem stating the existence of a “saddle point” can be interpreted as duality theorem for a pair of dual programs.
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https://doi.org/10.1007/978-3-642-46216-0Arithmetic; Convexity; Dimensions; Finite; Konvexe Planungsrechnung; Topology; algebra; function; geometry; t
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