变分分析 [Variational Analysis] pdf epub mobi txt 电子书 下载 2025

简体网页||繁体网页

☆☆☆☆☆

[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 Min
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

前言/序言

评分☆☆☆☆☆

好书，经典教材，看完有帮助

评分☆☆☆☆☆

不错的东西。。。。。。。。。。

评分☆☆☆☆☆

这是一本非常经典的教材，很是直接拥有，当成工具书也是很好的

评分☆☆☆☆☆

　　二十多年前，我刚到美国读书时，有一个流行的迷思（myth），就是认为中国人的数学要好过美国人，中国的数学教育要好过美国的数学教育。到了美国后才发现远不是那么回事，在文学院里数学最好的学生是美国人，在工学院里数学最好的学生是美国人，在数学系里最好的学生也还是美国人，而不是中国留学生。当然，偶尔也有例外，比如，若把北大清华毕业的学生放到美国连体育运动员都不屑去的社区学院时。真有本事，同加州理工或麻省理工的美国孩子比。想想看为什么到目前为止还没有中国人（或者更放宽一点，在中国受过教育的人）得到过菲尔茨奖或任何其它数学大奖，这个问题也许不难回答。是的，有一个丘成桐（Shing-Tung Yau），还有一个陶哲轩（Terence Tao），但他们不是中国人，受的也不是中国教育。不敢想象他们若是在中国，会受到什么样的摧残。

评分☆☆☆☆☆

好书！好书！

评分☆☆☆☆☆

这是一本非常经典的教材，很是直接拥有，当成工具书也是很好的

评分☆☆☆☆☆

非常不错，已经多次购买了！

评分☆☆☆☆☆

评分☆☆☆☆☆

非常不错，已经多次购买了！