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

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[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☆☆☆☆☆

变分分析的经典作品，强烈推荐相关专业学生学习使用！

评分☆☆☆☆☆

变分分析的经典作品，强烈推荐相关专业学生学习使用！

评分☆☆☆☆☆

书非常好，我会慢慢研读！

评分☆☆☆☆☆

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☆☆☆☆☆

看了几页 内容很专业 不过版式上看是本老教材

评分☆☆☆☆☆

书内容是好，里面对subdifferential刻画详细无出其右。但是世图能不能长点心？每次翻开这本书我得带个防毒面具吗？印刷质量已经不能用烂来形容了。简直是危害健康啊！~上打印的都比你质量好

评分☆☆☆☆☆

非常不错，已经多次购买了！