点击选择搜索分类
首页 - 地球物理学- 正文
☆☆☆☆☆
||
[美] 洛克菲勒(R.Tyrrell Rockafellar),[美] Roger J-B Wets 著
出版社: 世界图书出版公司 ISBN:9787510061363 版次:1 商品编码:11323592 包装:平装 外文名称:Variational Analysis 开本:24开 出版时间:2013-10-01 用纸:胶版纸 页数:734 正文语种:英文
For a long time, variational problems have been identified mostly with the 'calculus of variations'. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinite-dimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of 'variational principles'. Notions of perturbation, approximation and even generalized differentiability were extensively investigated, Variational theory progressed also to the study of so-called stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
A. Penalties and Constraints
B. Epigraphs and Semicontinuity
C. Attainment of a Minimum
D. Continuity, Closure and Growth
E. Extended Arithmetic
F. Parametric Dependence
G. Moreau Envelopes
H. Epi-Addition and Epi-Multiplication
I*. Auxiliary Facts and Principles
Commentary
Chapter 2. Convexity
A. Convex Sets and Functions
B. Level Sets and Intersections
C. Derivative Tests
D. Convexity in Operations
E. Convex Hulls
F. Closures and Contimuty
G.* Separation
H* Relative Interiors
I* Piecewise Linear Functions
J* Other Examples
Commentary
Chapter 3. Cones and Cosmic Closure
A. Direction Points
B. Horizon Cones
C. Horizon Functions
D. Coercivity Properties
E* Cones and Orderings
F* Cosmic Convexity
G* Positive Hulls
Commentary
Chapter 4. Set Convergence
A. Inner and Outer Limits
B. Painleve-Kuratowski Convergence
C. Pompeiu-Hausdorff Distance
D. Cones and Convex Sets
E. Compactness Properties
F. Horizon Limits
G* Contimuty of Operations
H* Quantification of Convergence
I* Hyperspace Metrics
Commentary
Chapter 5. Set-Valued Mappings
A. Domains, Ranges and Inverses
B. Continuity and Semicontimuty
C. Local Boundedness
D. Total Continuity
E. Pointwise and Graphical Convergence
F. Equicontinuity of Sequences
G. Continuous and Uniform Convergence
H* Metric Descriptions of Convergence
I* Operations on Mappings
J* Generic Continuity and Selections
Commentary .
Chapter 6. Variational Geometry
A. Tangent Cones
B. Normal Cones and Clarke Regularity
C. Smooth Manifolds and Convex Sets
D. Optimality and Lagrange Multipliers
E. Proximal Normals and Polarity
F. Tangent-Normal Relations
G* Recession Properties
H* Irregularity and Convexification
I* Other Formulas
Commentary
Chapter 7. Epigraphical Limits
A. Pointwise Convergence
B. Epi-Convergence
C. Continuous and Uniform Convergence
D. Generalized Differentiability
E. Convergence in Minimization
F. Epi-Continuity of Function-Valued Mappings
G. Continuity of Operations
H* Total Epi-Convergence
I* Epi-Distances
J* Solution Estimates
Commentary
Chapter 8. Subderivatives and Subgradients
A. Subderivatives of Functions
B. Subgradients of Functions
C. Convexity and Optimality
D. Regular Subderivatives
E. Support Functions and Subdifferential Duality
F. Calmness
G. Graphical Differentiation of Mappings
H* Proto-Differentiability and Graphical Regularity
I* Proximal Subgradients
J* Other Results
Commentary
Chapter 9. Lipschitzian Properties
A. Single-Valued Mappings
B. Estimates of the Lipschitz Modulus
C. Subdifferential Characterizations
D. Derivative Mappings and Their Norms
E. Lipschitzian Concepts for Set-Valued Mappings
……
Chapter 10. Subdifferential Calculus
Chapter 11. Dualization
Chapter 12. Monotone Mappings
Chapter 13. Second-Order Theory
Chapter 14. Measurability
变分分析 [Variational Analysis] 电子书 下载 mobi epub pdf txt
变分分析 [Variational Analysis]-so88
变分分析 [Variational Analysis] pdf epub mobi txt 电子书 下载 2022
图书介绍
☆☆☆☆☆
||
[美] 洛克菲勒(R.Tyrrell Rockafellar),[美] Roger J-B Wets 著
出版社: 世界图书出版公司 ISBN:9787510061363 版次:1 商品编码:11323592 包装:平装 外文名称:Variational Analysis 开本:24开 出版时间:2013-10-01 用纸:胶版纸 页数:734 正文语种:英文
内容简介
In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis refiects this breadth.For a long time, variational problems have been identified mostly with the 'calculus of variations'. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinite-dimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of 'variational principles'. Notions of perturbation, approximation and even generalized differentiability were extensively investigated, Variational theory progressed also to the study of so-called stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
目录
Chapter 1. Max and MinA. Penalties and Constraints
B. Epigraphs and Semicontinuity
C. Attainment of a Minimum
D. Continuity, Closure and Growth
E. Extended Arithmetic
F. Parametric Dependence
G. Moreau Envelopes
H. Epi-Addition and Epi-Multiplication
I*. Auxiliary Facts and Principles
Commentary
Chapter 2. Convexity
A. Convex Sets and Functions
B. Level Sets and Intersections
C. Derivative Tests
D. Convexity in Operations
E. Convex Hulls
F. Closures and Contimuty
G.* Separation
H* Relative Interiors
I* Piecewise Linear Functions
J* Other Examples
Commentary
Chapter 3. Cones and Cosmic Closure
A. Direction Points
B. Horizon Cones
C. Horizon Functions
D. Coercivity Properties
E* Cones and Orderings
F* Cosmic Convexity
G* Positive Hulls
Commentary
Chapter 4. Set Convergence
A. Inner and Outer Limits
B. Painleve-Kuratowski Convergence
C. Pompeiu-Hausdorff Distance
D. Cones and Convex Sets
E. Compactness Properties
F. Horizon Limits
G* Contimuty of Operations
H* Quantification of Convergence
I* Hyperspace Metrics
Commentary
Chapter 5. Set-Valued Mappings
A. Domains, Ranges and Inverses
B. Continuity and Semicontimuty
C. Local Boundedness
D. Total Continuity
E. Pointwise and Graphical Convergence
F. Equicontinuity of Sequences
G. Continuous and Uniform Convergence
H* Metric Descriptions of Convergence
I* Operations on Mappings
J* Generic Continuity and Selections
Commentary .
Chapter 6. Variational Geometry
A. Tangent Cones
B. Normal Cones and Clarke Regularity
C. Smooth Manifolds and Convex Sets
D. Optimality and Lagrange Multipliers
E. Proximal Normals and Polarity
F. Tangent-Normal Relations
G* Recession Properties
H* Irregularity and Convexification
I* Other Formulas
Commentary
Chapter 7. Epigraphical Limits
A. Pointwise Convergence
B. Epi-Convergence
C. Continuous and Uniform Convergence
D. Generalized Differentiability
E. Convergence in Minimization
F. Epi-Continuity of Function-Valued Mappings
G. Continuity of Operations
H* Total Epi-Convergence
I* Epi-Distances
J* Solution Estimates
Commentary
Chapter 8. Subderivatives and Subgradients
A. Subderivatives of Functions
B. Subgradients of Functions
C. Convexity and Optimality
D. Regular Subderivatives
E. Support Functions and Subdifferential Duality
F. Calmness
G. Graphical Differentiation of Mappings
H* Proto-Differentiability and Graphical Regularity
I* Proximal Subgradients
J* Other Results
Commentary
Chapter 9. Lipschitzian Properties
A. Single-Valued Mappings
B. Estimates of the Lipschitz Modulus
C. Subdifferential Characterizations
D. Derivative Mappings and Their Norms
E. Lipschitzian Concepts for Set-Valued Mappings
……
Chapter 10. Subdifferential Calculus
Chapter 11. Dualization
Chapter 12. Monotone Mappings
Chapter 13. Second-Order Theory
Chapter 14. Measurability
前言/序言
变分分析 [Variational Analysis] 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
- 恐龙-走进大自然百科图鉴
- 唯我独财--时尚女人理财经、拢财术
- BF-科学发现纵横谈-王梓坤 湖北科学技术出版社 9787535256171
- 女人恋物癖 兰小界著 9787221107473
- 爱做梦的爱因斯坦 (韩)宋恩英,(韩)申英宇 绘,张晟,牧华
- 分手笑忘书 出版社:人民邮电出版社 9787115290304
- 三只小猪-经典童话涂色游戏书
- 婚姻物语 家庭杂志社 9787806972106
- 自信让我更快乐(6-12岁首选校园文学励志读本)/小学生校园励志系列
- 招商银行:因您而变
- 正版新书--资源回收再利用(理论与实践) 吴鹏 重庆大学
- 正版 直击新三板(第二版) 北京是道可特律师事务所著 9787508650913
- 从粒子到宇宙:肉眼看不见的极美世界 天文航天 科普书籍
- 人身保险业务(学生用书) 9787509521038
- 写给中小学生的法布尔昆虫记 第十卷 的生活 9787542768438 法布尔(Fabre