- ISBN:9787510061363
- 装帧:一般胶版纸
- 册数:暂无
- 重量:暂无
- 开本:24开
- 页数:734
- 出版时间:2013-10-01
- 条形码:9787510061363 ; 978-7-5100-6136-3
本书特色
《变分分析》从该理论的*初起源——积分函数的*小化开始,对该理论做了较深的讨论。变分观点的发展很大程度上和优化、平衡、控制这些理论是紧密相关的。书中在一个统一的框架之中,全面讲述了经典分析和凸分析之外的变分几何和次微积分知识。也讲述了集收敛、集值映射和epi收敛、对偶和正则被积函数。本书由洛克菲勒著。
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
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
作者简介
R. Tyrrell Rockafellar, Roger J-B Wets是国际知名学者,在数学和物理学界享有盛誉。本书凝聚了作者多年科研和教学成果,适用于科研工作者、高校教师和研究生。
-
昆虫采集制作及主要目科简易识别手册
¥33.0¥50.0 -
中国少数民族人类起源神话研究
¥22.4¥66.0 -
物理学之美-插图珍藏版
¥22.1¥69.0 -
反物质世界的终极镜像
¥12.8¥20.0 -
数学的魅力;初等数学概念演绎
¥9.5¥22.0 -
昆虫的生存之道
¥14.4¥38.0 -
科学中的性别
¥18.5¥56.0 -
技术史入门
¥29.3¥48.0 -
现代物理学的概念和理论
¥31.3¥68.0 -
现代科技中的天文学
¥10.3¥13.0 -
星空探奇
¥26.9¥39.0 -
为了人人晓得相对论
¥3.9¥13.5 -
高等数学学习辅导(第4版)/马铭福
¥23.3¥33.8 -
科技卷-科技之光-国民教育通识读本
¥27.7¥39.8 -
数学中的循序逐增现象及其规律
¥29.3¥48.0 -
宇宙与人
¥11.2¥35.0 -
勒维特之星-大发现系列丛书
¥7.7¥16.0 -
生物化学与分子生物学实验
¥22.4¥32.0 -
费曼物理学讲义:新千年版:the new millennium edition:第3卷:volume Ⅲ
¥71.5¥98.0 -
数学文化
¥26.2¥38.0