作者:
Stephen Boyd
/
Lieven Vandenberghe
出版社: 世界图书出版公司
副标题: convex optimization
出版年: 2013-10-1
页数: 716
定价: 149.00
装帧: 平装
ISBN: 9787510061356
出版社: 世界图书出版公司
副标题: convex optimization
出版年: 2013-10-1
页数: 716
定价: 149.00
装帧: 平装
ISBN: 9787510061356
内容简介 · · · · · ·
《凸优化(英文)》由世界图书出版社出版。
作者简介 · · · · · ·
作者:(美国)鲍迪(Stephen Boyd)
目录 · · · · · ·
Preface
Introduction
1.1. Mathematical optimization
1.2 Least—squares and linear programming
1.3 Convex optimization
1.4 Nonlinear optimization
· · · · · · (更多)
Introduction
1.1. Mathematical optimization
1.2 Least—squares and linear programming
1.3 Convex optimization
1.4 Nonlinear optimization
· · · · · · (更多)
Preface
Introduction
1.1. Mathematical optimization
1.2 Least—squares and linear programming
1.3 Convex optimization
1.4 Nonlinear optimization
1.5 Outline
1.6 Notation
Bibliography
Theory
Convex sets
2.1 Affine and convex sets
2.2 Some important examples
2.3 Operations that preserve convexity
2.4 Generalized inequalities
2.5 Separating and supporting hyperplanes
2.6 Dual cones and generalized inequalities
Bibliography
Exercises
Convex functions
3.1 Basic properties and examples
3.2 Operations that preserve convexity
3.3 The conjugate function
3.4 Quasiconvex functions
3.5 Log—concave and log—convex functions
3.6 Convexity with respect to generalized inequalities
Bibliography
Exercises
Convex optimization problems
4.1 Optimization problems
4.2 Convex optimization
4.3 Linear optimization problems
4.4 Quadratic optimization problems
4.5 Geometric programming
4.6 Generalized inequality constraints
4.7 Vector optimization
Bibliography
Exercises
Duality
5.1 The Lagrange dual function
5.2 The Lagrange dual problem
5.3 Geometric interpretation
5.4 Saddle—point interpretation
5.5 Optimality conditions
5.0 Perturbation and sensitivity analysis
5.7 Examples
5.8 Theorems of alternatives
5,9 Generalized inequalities
Bibliography
Exercises
II Applications
6 Approximation and fitting
6.1 Norm approximation
0.2 Least—norm problems
6.3 Regularized approximation
6.4 Robust approximation
6.5 Function fitting and interpolation
Bibliography
Exercises
Statistical estimation
7.1 Parametric distribution estimation
7.2 Nonparametric distribution estimation
7.3 Optimal detector design and hypothesis testing
7.4 Chebyshev and Chernoff bounds
7.5 Experiment design
Bibliography
Exercises
8 Geometric problems
8.1 Projection on a set
8.2 Distance between sets
8.3 Euclidean distance and angle problems
8.4 Extremal volume ellipsoids
8.5 Centering
8.6 Classification
8.7 Placement and location
8.8 Floor planning
Bibliography
Exercises
III Algorithms
9 Unconstrained minimization
9.1 Unconstrained minimization problems
9.2 Descent methods
9.3 Gradient descent method
9.4 Steepest descent method
9.5 Newton's method
9.6 Self—concordance
9.7 Implementation
Bibliography
Exercises
10 Equality constrained minimization
10.1 Equality constrained minimization problems
10.2 Newton's method with equality constraints
10.3 Infeasible start Newton method
10.4 Implementation
Bibliography
Exercises
11 Interior—point methods
11.1 Inequality constrained minimization problems
11.2 Logarithmic barrier function and central path
11.3 The barrier method
11.4 Feasibility and phase I methods
11.5 Complexity analysis via self—concordance
11.6 Problems with generalized inequalities
11.7 Primal—dual interior—point methods
11.8 Implementation
Bibliography
Exercises
Appendices
A Mathematical background
A.1 Norms
A.2 Analysis
A.3 Functions
A.4 Derivatives
A.5 Linear algebra
Bibliography
B Problems involving two quadratic functions
B.1 Single constraint quadratic optimization
B.2 The S—procedure
B.3 The field of values of two symmetric matrices
B.4 Proofs of the strong duality results
Bibliography
C Numerical linear algebra background
C.1 Matrix structure and algorithm complexity
C.2 Solving linear equations with factored matrices
C.3 LU, Cholesky, and LDLT factorization
C.4 Block elimination and Schur complements
C.5 Solving underdetermined linear equations
Bibliography
References
Notation
Index
· · · · · · (收起)
Introduction
1.1. Mathematical optimization
1.2 Least—squares and linear programming
1.3 Convex optimization
1.4 Nonlinear optimization
1.5 Outline
1.6 Notation
Bibliography
Theory
Convex sets
2.1 Affine and convex sets
2.2 Some important examples
2.3 Operations that preserve convexity
2.4 Generalized inequalities
2.5 Separating and supporting hyperplanes
2.6 Dual cones and generalized inequalities
Bibliography
Exercises
Convex functions
3.1 Basic properties and examples
3.2 Operations that preserve convexity
3.3 The conjugate function
3.4 Quasiconvex functions
3.5 Log—concave and log—convex functions
3.6 Convexity with respect to generalized inequalities
Bibliography
Exercises
Convex optimization problems
4.1 Optimization problems
4.2 Convex optimization
4.3 Linear optimization problems
4.4 Quadratic optimization problems
4.5 Geometric programming
4.6 Generalized inequality constraints
4.7 Vector optimization
Bibliography
Exercises
Duality
5.1 The Lagrange dual function
5.2 The Lagrange dual problem
5.3 Geometric interpretation
5.4 Saddle—point interpretation
5.5 Optimality conditions
5.0 Perturbation and sensitivity analysis
5.7 Examples
5.8 Theorems of alternatives
5,9 Generalized inequalities
Bibliography
Exercises
II Applications
6 Approximation and fitting
6.1 Norm approximation
0.2 Least—norm problems
6.3 Regularized approximation
6.4 Robust approximation
6.5 Function fitting and interpolation
Bibliography
Exercises
Statistical estimation
7.1 Parametric distribution estimation
7.2 Nonparametric distribution estimation
7.3 Optimal detector design and hypothesis testing
7.4 Chebyshev and Chernoff bounds
7.5 Experiment design
Bibliography
Exercises
8 Geometric problems
8.1 Projection on a set
8.2 Distance between sets
8.3 Euclidean distance and angle problems
8.4 Extremal volume ellipsoids
8.5 Centering
8.6 Classification
8.7 Placement and location
8.8 Floor planning
Bibliography
Exercises
III Algorithms
9 Unconstrained minimization
9.1 Unconstrained minimization problems
9.2 Descent methods
9.3 Gradient descent method
9.4 Steepest descent method
9.5 Newton's method
9.6 Self—concordance
9.7 Implementation
Bibliography
Exercises
10 Equality constrained minimization
10.1 Equality constrained minimization problems
10.2 Newton's method with equality constraints
10.3 Infeasible start Newton method
10.4 Implementation
Bibliography
Exercises
11 Interior—point methods
11.1 Inequality constrained minimization problems
11.2 Logarithmic barrier function and central path
11.3 The barrier method
11.4 Feasibility and phase I methods
11.5 Complexity analysis via self—concordance
11.6 Problems with generalized inequalities
11.7 Primal—dual interior—point methods
11.8 Implementation
Bibliography
Exercises
Appendices
A Mathematical background
A.1 Norms
A.2 Analysis
A.3 Functions
A.4 Derivatives
A.5 Linear algebra
Bibliography
B Problems involving two quadratic functions
B.1 Single constraint quadratic optimization
B.2 The S—procedure
B.3 The field of values of two symmetric matrices
B.4 Proofs of the strong duality results
Bibliography
C Numerical linear algebra background
C.1 Matrix structure and algorithm complexity
C.2 Solving linear equations with factored matrices
C.3 LU, Cholesky, and LDLT factorization
C.4 Block elimination and Schur complements
C.5 Solving underdetermined linear equations
Bibliography
References
Notation
Index
· · · · · · (收起)
原文摘录 · · · · · ·
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凸优化的书评 · · · · · · ( 全部 11 条 )
最好的教材,最好的课程,没有之一
这本书主要是面向实际应用。书中提供了凸优化的理论框架,但不强调复杂的定理证明。丰富的实例是这本书的特色。实例涉及的领域非常广例如通信,金融,机器学习等等。 Stephen教授在个人主页上提供了免费电子版本,而且还包含了习题以及相关数据和程序的下载。课程的讲义也可...
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一本凸规划问题的实用教程
看起来是厚厚的一本大部头,读起来并不太费力。它给出的实例多而好用、覆盖面全,不需要太深刻的数学功底,对于复杂的定理性质等也不强调证明,而是着眼于几何意义和实际用途,直观易懂。 作者本身的工科背景使得这本书在工业问题和计算机等实用方面的优点更为突出,数学依据...
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maybe you would have known ..
Copyright in this book is held by Cambridge University Press, who have kindly agreed to allow us to keep the book available on the web. http://www.stanford.edu/~boyd/cvxbook/ you will find e-book and the exercises answer book. Cheers --- All the conte...
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英文原版资源和书中习题答案、python代码下载
扫码关注公众号 「图灵的猫」,点击“学习资料”菜单,可以获得海量python、机器学习、深度学习书籍、课程资源,以及书中对应习题答案和代码。后台回复SSR更有机场节点相送~ 我总结了深度学习、机器学习领域中所有会用到的数学知识,大家在制定计划时可以以这些知识点为脉络进...
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> 更多书评 11篇
论坛 · · · · · ·
在这本书的论坛里发言这本书的其他版本 · · · · · · ( 全部4 )
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Cambridge University Press (2004)9.6分 426人读过
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Cambridge India (2016)暂无评分 2人读过
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清华大学出版社 (2013)9.4分 193人读过
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订阅关于凸优化的评论:
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0 有用 段干相若 2022-03-28 22:15:02
一边与中文版对着学,终于把这本书完完整整地啃了一遍,收获的绝不仅仅是书中的推导与结论,而是数学模型的思想与数学语言的熟悉。至于本书知识的意义,作为应用数学,可以应用的地方实在是太多,花了半个月的闲暇时间打牢基础的投入绝对是值得的!
0 有用 Bowser 2024-02-28 10:15:19 上海
《人工智能的数学基础》后半部分凸优化的教材,老师不按照教材讲,全英文自己啃也啃不动,英语的证明逻辑跟中文差别很多,证明思路相反,两方面都有原因吧,最后读下来感觉不好
0 有用 儒豪 2023-08-08 02:17:05 上海
虽然很多人称赞。 但我仍然觉得这样的内容编排、动不动就疯狂罗列令人十分不适。
3 有用 杜松子 2020-04-22 18:05:35
B站拯救了我
0 有用 谭画 2017-11-18 13:07:45
经典
0 有用 Bowser 2024-02-28 10:15:19 上海
《人工智能的数学基础》后半部分凸优化的教材,老师不按照教材讲,全英文自己啃也啃不动,英语的证明逻辑跟中文差别很多,证明思路相反,两方面都有原因吧,最后读下来感觉不好
0 有用 儒豪 2023-08-08 02:17:05 上海
虽然很多人称赞。 但我仍然觉得这样的内容编排、动不动就疯狂罗列令人十分不适。
0 有用 段干相若 2022-03-28 22:15:02
一边与中文版对着学,终于把这本书完完整整地啃了一遍,收获的绝不仅仅是书中的推导与结论,而是数学模型的思想与数学语言的熟悉。至于本书知识的意义,作为应用数学,可以应用的地方实在是太多,花了半个月的闲暇时间打牢基础的投入绝对是值得的!
3 有用 杜松子 2020-04-22 18:05:35
B站拯救了我
0 有用 谭画 2017-11-18 13:07:45
经典