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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變分分析的經典作品，強烈推薦相關專業學生學習使用！

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　　不可否認，美國人學工程及數學的人確實越來越少，學商及法律的人也越來越多，但這並不意味著一個普通的（average）受過教育的美國人的數學水平要低於一個普通的受過教育的中國人。即使是在美國的商學院、法學院裏數學好的學生肯定也是美國人。這是因為美國的中學提倡的是通纔教育，高中的數學是有一定標準的，並且數學中強調邏輯與推理的訓練。而中國的學生初中畢業就開始文理分科，其結果是美國最爛的高中畢業的學生的數學水平也要比中國最好的大學畢業的文科博士高很多。美國的正規學校，初中以前基本放羊，但一到高中，立刻嚴謹。美國一個正規高中學生受到的學業壓力不比中國孩子輕。一個普通的中國人在他（她）受教育的過程中，隻有在初中以前，有可能有機會比美國人數學好。

評分☆☆☆☆☆

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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