變分分析 [Variational Analysis] 下載 mobi epub pdf 電子書 2024

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內容簡介

　　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.

目錄

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

變分分析 [Variational Analysis] 下載 mobi epub pdf txt 電子書 格式

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不錯的東西。。。。。。。。。。

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　　二十多年前，我剛到美國讀書時，有一個流行的迷思（myth），就是認為中國人的數學要好過美國人，中國的數學教育要好過美國的數學教育。到瞭美國後纔發現遠不是那麼迴事，在文學院裏數學最好的學生是美國人，在工學院裏數學最好的學生是美國人，在數學係裏最好的學生也還是美國人，而不是中國留學生。當然，偶爾也有例外，比如，若把北大清華畢業的學生放到美國連體育運動員都不屑去的社區學院時。真有本事，同加州理工或麻省理工的美國孩子比。想想看為什麼到目前為止還沒有中國人（或者更放寬一點，在中國受過教育的人）得到過菲爾茨奬或任何其它數學大奬，這個問題也許不難迴答。是的，有一個丘成桐（Shing-Tung Yau），還有一個陶哲軒（Terence Tao），但他們不是中國人，受的也不是中國教育。不敢想象他們若是在中國，會受到什麼樣的摧殘。

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古希臘時，柏拉圖學院的門口戳瞭快牌子“不懂幾何的彆進來”。柏老師意思很簡單：我這兒是講道理的地方，你丫要是妄想像中國人那樣鬍攪蠻纏，哪涼快哪呆著去！當然你非要把這塊牌子理解成“華人與狗不得入內”，我也找不齣反駁的理由，因為普遍地說中國人至今還沒認同講道理是構成文明的一個根本要素。柏老師這種對基本數學和邏輯知識的尊重的傳統至今還保留在西方教育係統中。

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