凸优化理论
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作者[美] 博赛克斯（Dimitri P.Bertsekas）
出版社清华大学出版社
ISBN9787302237600
出版时间2011-01
版次1
装帧平装
开本16开
纸张胶版纸
页数494页
定价59元
上书时间2024-07-01
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基本信息
书名:凸优化理论
定价：59元
作者:[美] 博赛克斯（Dimitri P.Bertsekas） 著
出版社：清华大学出版社
出版日期：2011-01-01
ISBN：9787302237600
字数：
页码：494
版次：1
装帧：平装
开本：16开
商品重量：
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内容提要
《凸优化理论（）》作者德梅萃·博赛克斯教授是优化理论的国际知名学者，现任美国麻省理工学院电气工程与计算机科学系教授，曾在斯坦福大学工程经济系和伊利诺伊大学电气工程系任教，在优化理论、控制工程、通信工程、计算机科学等领域有丰富的科研教学经验，成果丰硕。博赛克斯教授是一位多产作者，著有14本专著和教科书。《凸优化理论（）》是作者在优化理论与方法的系列专著和教科书中的一本，自成体系又相互对应。主要内容分为两部分：凸分析和凸问题的对偶优化理论。
目录
1 Basic Concepts of Convex Analysis1.1 Convex Sets and Functions1.1.1 Convex Functions1.1.2 Closedness and Semicontinuity1.1.3 Operations with Convex Functions1.1.4 Characterizations of Differentiable Convex Functions1.2 Convex and Affine Hulls1.3 Relative Interior and Closure1.3.1 Calculus of Relative Interiors and Closures1.3.2 Continuity of Convex Functions1.3.3 Closures of Functions1.4 RecessioCones1.4.1 Directions of Recessioof a Convex Function1.4.2 Nonemptine~s of Intersections of Closed Sets1.4.3 Closedness Under Linear Transformations1.5 Hyperplanes1.5.1 Hyperplane Separation1.5.2 Proper Hyperplane Separation1.5.3 Nonvertical Hyperplane Separation1.6 Conjugate Functions1.7 Summary2 Basic Concepts of Polyhedral Convety2.1 Extreme Points2.2 Polar Cones2.3 Polyhedral Sets and Functions2.3.1 Polyhedral Cones and Farkas' Lemma2.3.2 Structure of Polyhedral Sets2.3.3 Polyhedral Functions2.4 Polyhedral Aspects of Optimization3 Basic Concepts of Convex Optimization3.1 Constrained Optimization3.2 Estence of Optimal Solutions3.3 Partial Minimizatioof Convex Functions3.4 Saddle Point and Minimax Theory4 Geometric Duality Framework4.1 MiCommon/Max Crossing Duality4.2 Some Special Cases4.2.1 Connectioto Conjugate Convex Functions4.2.2 General OptimizatioDuality4.2.3 Optimizatiowith Inequality Constraints4.2.4 Augmented LagrangiaDuality4.2.5 Minimax Problems4.3 Strong Duality Theorem4.4 Estence of Dual Optimal Solutions4.5 Duality and Polyhedral Convety4.6 Summary5 Duality and Optimization5.1 Nonlinear Farkas' Lemma5.2 Linear Programming Duality5.3 Convex Programming Duality5.3.1 Strong Duality Theorem - Inequality.Constraints5.3.2 Optimality Conditions5.3.3 Partially Polyhedral Constraints5.3.4 Duality and Estence of Optimal Primal Solutions5.3.5 Fenchel Duality5.3.6 Conic Duality5.4 Subgradients and Optimality Conditions5.4.1 Subgradients of Conjugate Functions5.4.2 Subdifferential Calculus5.4.3 Optimality Conditions5.4.4 Directional Derivatives5.5 Minimax Theory5.5.1 Minimax Duality Theorems5.5.2 Saddle Point Theorems5.6 Theorems of the Alternative5.7 Nonconvex Problems5.7.1 Duality Gap iSeparable Problems5.7.2 Duality Gap iMinimax ProblemsAppendix A： Mathematical BackgroundNotes and SourcesSupplementary Chapter 6 oConvex OptimizatioAlgorithms
作者介绍
序言
1 Basic Concepts of Convex Analysis1.1 Convex Sets and Functions1.1.1 Convex Functions1.1.2 Closedness and Semicontinuity1.1.3 Operations with Convex Functions1.1.4 Characterizations of Differentiable Convex Functions1.2 Convex and Affine Hulls1.3 Relative Interior and Closure1.3.1 Calculus of Relative Interiors and Closures1.3.2 Continuity of Convex Functions1.3.3 Closures of Functions1.4 RecessioCones1.4.1 Directions of Recessioof a Convex Function1.4.2 Nonemptine~s of Intersections of Closed Sets1.4.3 Closedness Under Linear Transformations1.5 Hyperplanes1.5.1 Hyperplane Separation1.5.2 Proper Hyperplane Separation1.5.3 Nonvertical Hyperplane Separation1.6 Conjugate Functions1.7 Summary2 Basic Concepts of Polyhedral Convexity2.1 Extreme Points2.2 Polar Cones2.3 Polyhedral Sets and Functions2.3.1 Polyhedral Cones and Farkas' Lemma2.3.2 Structure of Polyhedral Sets2.3.3 Polyhedral Functions2.4 Polyhedral Aspects of Optimization3 Basic Concepts of Convex Optimization3.1 Constrained Optimization3.2 Existence of Optimal Solutions3.3 Partial Minimizatioof Convex Functions3.4 Saddle Point and Minimax Theory4 Geometric Duality Framework4.1 MiCommon/Max Crossing Duality4.2 Some Special Cases4.2.1 Connectioto Conjugate Convex Functions4.2.2 General OptimizatioDuality4.2.3 Optimizatiowith Inequality Constraints4.2.4 Augmented LagrangiaDuality4.2.5 Minimax Problems4.3 Strong Duality Theorem4.4 Existence of Dual Optimal Solutions4.5 Duality and Polyhedral Convexity4.6 Summary5 Duality and Optimization5.1 Nonlinear Farkas' Lemma5.2 Linear Programming Duality5.3 Convex Programming Duality5.3.1 Strong Duality Theorem - Inequality.Constraints5.3.2 Optimality Conditions5.3.3 Partially Polyhedral Constraints5.3.4 Duality and Existence of Optimal Primal Solutions5.3.5 Fenchel Duality5.3.6 Conic Duality5.4 Subgradients and Optimality Conditions5.4.1 Subgradients of Conjugate Functions5.4.2 Subdifferential Calculus5.4.3 Optimality Conditions5.4.4 Directional Derivatives5.5 Minimax Theory5.5.1 Minimax Duality Theorems5.5.2 Saddle Point Theorems5.6 Theorems of the Alternative5.7 Nonconvex Problems5.7.1 Duality Gap iSeparable Problems5.7.2 Duality Gap iMinimax ProblemsAppendix A： Mathematical BackgroundNotes and SourcesSupplementary Chapter 6 oConvex OptimizatioAlgorithms
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