| 书名 | 凸分析 |
| 分类 | 科学技术-自然科学-数学 |
| 作者 | (德)洛克菲拉 |
| 出版社 | 世界图书出版公司 |
| 下载 | 抱歉，不提供下载，请购买正版图书。 |
| 简介 | 编辑推荐 Convexity has been increasingly important in recent years in the studyof extremum problems in ,many areas of applied mathematics. The purposeof this book is to provide an exposition of the theory of convex sets andfunctions in which applications to extremum problems play the centralrole. 目录 Preface Introductory Remarks：a Guide for the Reader PART Ⅰ：BASIC CONCEPTS §1.Affine Sets §2.Convex Sets and Cones §3.The Algebra of Convex Sets §4.Convex Functions §5.Functional Operations PART Ⅱ：TOPOLOGICAL PROPERTIES §6.Relative Interiors of Convex Sets §7.Closures of Convex Functions §8.Recession Cones and Unboundedness §9.Some Closedness Criteria §10.Continuity of Convex Functions PART Ⅲ：DUALITY CORRESPONDENCES §11.Separation Theorems §i2.Conjugates of Convex Functions §13.Support Functions §14.Polars of Convex Sets §15.Polars of Convex Functions §16.Dual Operations PART Ⅳ：REPRESENTATION AND INEQUALITIES §i7.Caratheodory's Theorem §18.Extreme Points and Faces of Convex Sets §19.Polyhedral Convex Sets and Functions §20.Some Applications of Polyhedral Convexity §21.Helly's Theorem and Systems of Inequalities §22.Linear Inequalities PART Ⅴ：DIFFERENTIAL THEORY §23.Directional Derivatives and Subgradients §24.Differential Continuity and Monotonicity §25.Differentiability of Convex Functions §26.The Legendre Transformation PART Ⅵ：CONSTRAINED EXTREMUM PROBLEMS §27.The Minimum of a Convex Function §28.Ordinary Convex Programs and Lagrange Multipliers §29.Bifunctions and Generalized Convex Programs §30.Adjoint Bifunctions and Dual Programs §31.Fenchers Duality Theorem §32.The Maximum of a Convex Function PART Ⅶ：SADDLE-FUNCTIONS AND MINIMAX THEORY §33.Saddle-Functions §34.Closures and Equivalence Classes §35.Continuity and Differentiability of Saddle-functions §36.Minimax Problems §37.Conjugate Saddle-functions and Minimax Theorems PART Ⅷ：CONVEX ALGEBRA §38.The Algebra of Bifunctions §39.Convex Processes Comments and References Bibliography Index |
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