| 书目名称 | Convexity and Optimization in Finite Dimensions I | | 编辑 | Josef Stoer,Christoph Witzgall | | 视频video | | | 丛书名称 | Grundlehren der mathematischen Wissenschaften | | 图书封面 |  | | 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 | | 关键词 | Arithmetic; Convexity; Dimensions; Finite; Konvexe Planungsrechnung; Topology; algebra; function; geometry; t | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-46216-0 | | isbn_softcover | 978-3-642-46218-4 | | isbn_ebook | 978-3-642-46216-0Series ISSN 0072-7830 Series E-ISSN 2196-9701 | | issn_series | 0072-7830 | | copyright | Springer-Verlag Berlin · Heidelberg 1970 |
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发表于 2025-3-21 19:18:44
