点击选择搜索分类
首页 - 国画赏析- 正文
☆☆☆☆☆
||
Dimitri,P.Bertsekas 著
出版社: 清华大学出版社 ISBN:9787302430704 版次:1 商品编码:11944450 包装:平装 丛书名: 清华版双语教学用书 外文名称:Convex Optimization Algorithms 开本:16开 出版时间:2016-05-01 用纸:胶版纸 页数:564 字数:623000 正文语种:中文
这些方法通常依赖于代价函数和约束条件的凸性(而不一定依赖于其可微性),并与对偶性有着直接或问接的联系。作者针对具体问题的特定结构,给出了大量的例题,来充分展示算法的应用。各章的内容如下:第一章,凸优化模型概述;第2章,优化算法概述;第3章,次梯度算法;第4章,多面体逼近算法;第5章,邻近算法;第6章,其他算法问题。《凸优化算法》的一个特色是在强调问题之间的对偶性的同时,也十分重视建立在共轭概念上的算法之间的对偶性,这常常能为选择合适的算法实现方式提供新的灵感和计算上的便利。
《凸优化算法》均取材于作者过去15年在美国麻省理工学院的凸优化方面课堂教学的内容。《凸优化算法》和《凸优化理论》这两《凸优化算法》合起来可以作为一个学期的凸优化课程的教材;《凸优化算法》也可以用作非线性规划课程的补充材料。
1.1. Lagrange Duality
1.1.1. Separable Problems - Decomposition
1.1.2. Partitioning
1.2. Fenchel Duality and Conic Programming
1.2.1. Linear Conic Problems
1.2.2. Second Order Cone Programming
1.2.3. Semidefinite Programming
1.3. Additive Cost Problems
1.4. Large Number of Constraints
1.5. Exact Penalty ~nctions
1.6. Notes, Sources, and Exercises
2. Optimization Algorithms: An Overview
2.1. Iterative Descent Algorithms
2.1.1. Differentiable Cost Function Descent - Unconstrained Problems
2.1.2. Constrained Problems - Feasible Direction Methods
2.1.3. Nondifferentiable Problems - Subgradient Methods
2.1.4. Alternative Descent Methods
2.1.5. Incremental Algorithms
2.1.6. Distributed Asynchronous Iterative Algorithms
2.2. Approximation Methods
2.2.1. Polyhedral Approximation
2.2.2. Penalty, Augmented Lagrangian, and Interior Point Methods
2.2.3. Proximal Algorithm, Bundle Methods, and Tikhonov Regularization
2.2.4. Alternating Direction Method of Multipliers
2.2.5. Smoothing of Nondifferentiable Problems
2.3. Notes, Sources, and Exercises
3. Subgradient Methods
3.1. Subgradients of Convex Real-Valued Functions
3.1.1. Characterization of the Subdifferential
3.2. Convergence Analysis of Subgradient Methods
3.3. e-Subgradient Methods
3.3.1. Connection with Incremental Subgradient Methods
3.4. Notes, Sources, and Exercises
4. Polyhedral Approximation Methods
4.1. Outer Linearization Cutting Plane Methods
4.2. Inner Linearization - Simplicial Decomposition
4.3. Duality of Outer and Inner Linearization
4.4. Generalized Polyhedral Approximation
4.5. Generalized Simplicial Decomposition
4.5.1. Differentiable Cost Case
4.5.2. Nondifferentiable Cost and Side Constraints
4.6. Polyhedral Approximation for Conic Programming
4.7. Notes, Sources, and Exercises
5. Proximal Algorithms
5.1. Basic Theory of Proximal Algorithms
5.1.1. Convergence
5.1.2. Rate of Convergence
5.1.3. Gradient Interpretation
5.1.4. Fixed Point Interpretation, Overrelaxation and Generalization
5.2. Dual Proximal Algorithms
5.2.1. Augmented Lagrangian Methods
5.3. Proximal Algorithms with Linearization
5.3.1. Proximal Cutting Plane Methods
5.3.2. Bundle Methods
5.3.3. Proximal Inner Linearization Methods
5.4. Alternating Direction Methods of Multipliers
5.4.1. Applications in Machine Learning
5.4.2. ADMM Applied to Separable Problems
5.5. Notes, Sources, and Exercises
6. Additional Algorithmic Topics
6.1. Gradient Projection Methods
6.2. Gradient Projection with Extrapolation
6.2.1. An Algorithm with Optimal Iteration Complexity
6.2.2. Nondifferentiable Cost Smoothing
6.3. Proximal Gradient Methods
6.4. Incremental Subgradient Proximal Methods
6.4.1. Convergence for Methods with Cyclic Order
6.4.2. Convergence for Methods with Randomized Order
6.4.3. Application in Specially Structured Problems
6.4.4. Incremental Constraint Projection Methods
6.5. Coordinate Descent Methods
6.5.1. Variants of Coordinate Descent
6.5.2. Distributed Asynchronous Coordinate Descent
6.6. Generalized Proximal Methods
6.7. e-Descent and Extended Monotropic Programming
6.7.1. e-Subgradients
6.7.2. e-Descent Method
6.7.3. Extended Monotropic Programming Duality
6.7.4. Special Cases of Strong Duality
6.8. Interior Point Methods
6.8.1. Primal-Dual Methods for Linear Programming
6.8.2. Interior Point Methods for Conic Programming
6.8.3. Central Cutting Plane Methods
6.9. Notes, Sources, and Exercises
Appendix A" Mathematical Background
A.1. Linear Algebra
A.2. Topological Properties
A.3. Derivatives
A.4. Convergence Theorems
Appendix B: Convex Optimization Theory: A Summary
B.1. Basic Concepts of Convex Analysis
B.2. Basic Concepts of Polyhedral Convexity
B.3. Basic Concepts of Convex Optimization
B.4. Geometric Duality Framework
B.5. Duality and Optimization
References
Index
凸优化算法 [Convex Optimization Algorithms] 电子书 下载 mobi epub pdf txt
凸优化算法 [Convex Optimization Algorithms]-so88
凸优化算法 [Convex Optimization Algorithms] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
Dimitri,P.Bertsekas 著
出版社: 清华大学出版社 ISBN:9787302430704 版次:1 商品编码:11944450 包装:平装 丛书名: 清华版双语教学用书 外文名称:Convex Optimization Algorithms 开本:16开 出版时间:2016-05-01 用纸:胶版纸 页数:564 字数:623000 正文语种:中文
内容简介
《凸优化算法》几乎囊括了所有主流的凸优化算法。包括梯度法、次梯度法、多面体逼近法、邻近法和内点法等。这些方法通常依赖于代价函数和约束条件的凸性(而不一定依赖于其可微性),并与对偶性有着直接或问接的联系。作者针对具体问题的特定结构,给出了大量的例题,来充分展示算法的应用。各章的内容如下:第一章,凸优化模型概述;第2章,优化算法概述;第3章,次梯度算法;第4章,多面体逼近算法;第5章,邻近算法;第6章,其他算法问题。《凸优化算法》的一个特色是在强调问题之间的对偶性的同时,也十分重视建立在共轭概念上的算法之间的对偶性,这常常能为选择合适的算法实现方式提供新的灵感和计算上的便利。
《凸优化算法》均取材于作者过去15年在美国麻省理工学院的凸优化方面课堂教学的内容。《凸优化算法》和《凸优化理论》这两《凸优化算法》合起来可以作为一个学期的凸优化课程的教材;《凸优化算法》也可以用作非线性规划课程的补充材料。
作者简介
德梅萃·博塞克斯(Dimitri P.Bertsekas),教授是优化理论的国际学者、美国国家工程院院士,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。博塞克斯教授是一位多产作者,著有14本专著和教科书。目录
1. Convex Optimization Models: An Overview1.1. Lagrange Duality
1.1.1. Separable Problems - Decomposition
1.1.2. Partitioning
1.2. Fenchel Duality and Conic Programming
1.2.1. Linear Conic Problems
1.2.2. Second Order Cone Programming
1.2.3. Semidefinite Programming
1.3. Additive Cost Problems
1.4. Large Number of Constraints
1.5. Exact Penalty ~nctions
1.6. Notes, Sources, and Exercises
2. Optimization Algorithms: An Overview
2.1. Iterative Descent Algorithms
2.1.1. Differentiable Cost Function Descent - Unconstrained Problems
2.1.2. Constrained Problems - Feasible Direction Methods
2.1.3. Nondifferentiable Problems - Subgradient Methods
2.1.4. Alternative Descent Methods
2.1.5. Incremental Algorithms
2.1.6. Distributed Asynchronous Iterative Algorithms
2.2. Approximation Methods
2.2.1. Polyhedral Approximation
2.2.2. Penalty, Augmented Lagrangian, and Interior Point Methods
2.2.3. Proximal Algorithm, Bundle Methods, and Tikhonov Regularization
2.2.4. Alternating Direction Method of Multipliers
2.2.5. Smoothing of Nondifferentiable Problems
2.3. Notes, Sources, and Exercises
3. Subgradient Methods
3.1. Subgradients of Convex Real-Valued Functions
3.1.1. Characterization of the Subdifferential
3.2. Convergence Analysis of Subgradient Methods
3.3. e-Subgradient Methods
3.3.1. Connection with Incremental Subgradient Methods
3.4. Notes, Sources, and Exercises
4. Polyhedral Approximation Methods
4.1. Outer Linearization Cutting Plane Methods
4.2. Inner Linearization - Simplicial Decomposition
4.3. Duality of Outer and Inner Linearization
4.4. Generalized Polyhedral Approximation
4.5. Generalized Simplicial Decomposition
4.5.1. Differentiable Cost Case
4.5.2. Nondifferentiable Cost and Side Constraints
4.6. Polyhedral Approximation for Conic Programming
4.7. Notes, Sources, and Exercises
5. Proximal Algorithms
5.1. Basic Theory of Proximal Algorithms
5.1.1. Convergence
5.1.2. Rate of Convergence
5.1.3. Gradient Interpretation
5.1.4. Fixed Point Interpretation, Overrelaxation and Generalization
5.2. Dual Proximal Algorithms
5.2.1. Augmented Lagrangian Methods
5.3. Proximal Algorithms with Linearization
5.3.1. Proximal Cutting Plane Methods
5.3.2. Bundle Methods
5.3.3. Proximal Inner Linearization Methods
5.4. Alternating Direction Methods of Multipliers
5.4.1. Applications in Machine Learning
5.4.2. ADMM Applied to Separable Problems
5.5. Notes, Sources, and Exercises
6. Additional Algorithmic Topics
6.1. Gradient Projection Methods
6.2. Gradient Projection with Extrapolation
6.2.1. An Algorithm with Optimal Iteration Complexity
6.2.2. Nondifferentiable Cost Smoothing
6.3. Proximal Gradient Methods
6.4. Incremental Subgradient Proximal Methods
6.4.1. Convergence for Methods with Cyclic Order
6.4.2. Convergence for Methods with Randomized Order
6.4.3. Application in Specially Structured Problems
6.4.4. Incremental Constraint Projection Methods
6.5. Coordinate Descent Methods
6.5.1. Variants of Coordinate Descent
6.5.2. Distributed Asynchronous Coordinate Descent
6.6. Generalized Proximal Methods
6.7. e-Descent and Extended Monotropic Programming
6.7.1. e-Subgradients
6.7.2. e-Descent Method
6.7.3. Extended Monotropic Programming Duality
6.7.4. Special Cases of Strong Duality
6.8. Interior Point Methods
6.8.1. Primal-Dual Methods for Linear Programming
6.8.2. Interior Point Methods for Conic Programming
6.8.3. Central Cutting Plane Methods
6.9. Notes, Sources, and Exercises
Appendix A" Mathematical Background
A.1. Linear Algebra
A.2. Topological Properties
A.3. Derivatives
A.4. Convergence Theorems
Appendix B: Convex Optimization Theory: A Summary
B.1. Basic Concepts of Convex Analysis
B.2. Basic Concepts of Polyhedral Convexity
B.3. Basic Concepts of Convex Optimization
B.4. Geometric Duality Framework
B.5. Duality and Optimization
References
Index
凸优化算法 [Convex Optimization Algorithms] 电子书 下载 mobi epub pdf txt
电子书下载地址:
相关电子书推荐:
- 文件名
- 解读身边的奥秘—生活中的自然知识 本册冯翀
- 单兵装备007
- 北极光科幻故事丛书 “雨”绿撒哈拉
- 三十六计全集/中华传统文化核心读本
- 你不可不知的50个物理知识
- 寻找公共政策的制度逻辑
- {RT}贝壳博物馆-[美] M·G·哈拉塞维奇,[美] 法比奥·莫尔 北京大学出版社 97
- 轻兵器100年(下)(修订版) [SMALL ARMS 1945-PRES]
- 丹青集粹
- 问道:改革开放以来的社会思潮与青年思想政治教育研究
- 推动丛书综合系列:复杂 [美] 梅拉妮米歇尔
- 不要成为下一个:腐败分子警示录/《中国纪检监察报》优秀作品集萃丛书
- 你不可不知的50个数学知识(50篇精炼的小文章,50个经典数学概念)
- 轻轻松松学养兔
- 狡猾的发明 绝妙的机器 [英]格里贝利