变分分析 [Variational Analysis] epub pdf mobi txt 电子书 下载 2024

变分分析 [Variational Analysis] epub pdf mobi txt 电子书 下载 2024

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变分分析 [Variational Analysis] epub pdf mobi txt 电子书 下载 2024

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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

变分分析 [Variational Analysis] epub pdf mobi txt 电子书 下载 2024

变分分析 [Variational Analysis] 下载 epub mobi pdf txt 电子书 2024

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评分☆☆☆☆☆

　　不可否认，美国人学工程及数学的人确实越来越少，学商及法律的人也越来越多，但这并不意味着一个普通的（average）受过教育的美国人的数学水平要低于一个普通的受过教育的中国人。即使是在美国的商学院、法学院里数学好的学生肯定也是美国人。这是因为美国的中学提倡的是通才教育，高中的数学是有一定标准的，并且数学中强调逻辑与推理的训练。而中国的学生初中毕业就开始文理分科，其结果是美国最烂的高中毕业的学生的数学水平也要比中国最好的大学毕业的文科博士高很多。美国的正规学校，初中以前基本放羊，但一到高中，立刻严谨。美国一个正规高中学生受到的学业压力不比中国孩子轻。一个普通的中国人在他（她）受教育的过程中，只有在初中以前，有可能有机会比美国人数学好。

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