《隱函式和解映射(英文)》在經典框架及其外研究隱函式的本質，主要側重於研究變分問題解映射的性質。《隱函式和解映射(英文)》自稱體系，並將大量散落的材料綜合起來，旨在提供一個研究這門學科的參考書籍。第一章以一種學生和本科生微積分的老師新聞樂見的方式講述經典隱函式定理，以下的章節在難度上逐漸增加，將隱映射看作是一種關聯定義的，而非方程定義的。書中講述了數值分析和最佳化中的套用。
基本介紹
- 書名：隱函式和解映射
- 作者：鄧契夫 (Asen L.Dontchev)
- 出版日期：2013年3月1日
- 語種：簡體中文, 英語
- ISBN：9787510058073
- 品牌：世界圖書出版公司北京公司
- 外文名：Implicit Functions and Solution Mappings
- 出版社：世界圖書出版公司北京公司
- 頁數：375頁
- 開本：24
- 定價：59.00
基本介紹,內容簡介,作者簡介,圖書目錄,
基本介紹
內容簡介
《隱函式和解映射(英文)》是本學科學術上的巨大成果，注定會成為這門學科的一本標準參考書。
作者簡介
作者：（美國）鄧契夫（Asen L.Dontchev）
圖書目錄
Preface
Acknowledgements
Chapter 1. Functions defined implicitly by equations
1A. The classical inverse function theorem
lB. The classical implicit function theorem
1C. Calmness
1D. Lipschitz continuity
I E. Lipschitz invertibility from approximations
I E Selections of multi-valued inverses
IG. Selections from nonstrict differentiability
Chapter 2. Implicit function theorems for variational problems
2A. Generalized equations and variational problems
2B. Implicit function theorems for generalized equations
2C. Ample parameterization and parametric robustness
2D. Semidifferentiable functions
2E. Variational inequalities with polyhedral convexity
2E Variational inequalities with monotonicity
2G. Consequences for optimization
Chapter 3. Regularity properties of set-valued solution mappings
3A. Set convergence
3B. Continuity of set-valued mappings
3C. Lipschitz continuity of set-valued mappings
3D. Outer Lipschitz continuity
3E. Aubin property, metric regularity and linear openness
3F. Implicit mapping theorems with metric regularity
3G. Strong metric regularity
3H. Calmness and metric subregularity
31. Strong metric subregularity
Chapter 4. Regularity properties through generalized derivatives
4A. Graphical differentiation
4B. Derivative criteria for the Aubin property
4C. Characterization of strong metric subregularity
4D. Applications to parameterized constraint systems
4E. Isolated calmness for variational inequalities
4F. Single-valued Idealizations for variational inequalities
4G. Special nonsmooth inverse function theorems
4H. Results utilizing coderivatives
Chapter 5. Regularity in infinite dimensions
5A. Openness and positively homogeneous mappings
5B. Mappings with closed and convex graphs
5C. Sublinear mappings
5D. The theorems of Lyusternik and Graves
5E. Metric regularity in metric spaces
5V. Strong metric regularity and implicit function theorems
5G. The Bartle-Graves theorem and extensions
Chapter 6. Applications in numerical variational analysis
6A. Radius theorems and conditioning
6B. Constraints and feasibility
6C. Iterative processes for generalized equations
6D. An implicit function theorem for Newton's iteration
6E. Galerkin's method for quadratic minimization
6F. Approximations in optimal control
References
Notation
Index
Acknowledgements
Chapter 1. Functions defined implicitly by equations
1A. The classical inverse function theorem
lB. The classical implicit function theorem
1C. Calmness
1D. Lipschitz continuity
I E. Lipschitz invertibility from approximations
I E Selections of multi-valued inverses
IG. Selections from nonstrict differentiability
Chapter 2. Implicit function theorems for variational problems
2A. Generalized equations and variational problems
2B. Implicit function theorems for generalized equations
2C. Ample parameterization and parametric robustness
2D. Semidifferentiable functions
2E. Variational inequalities with polyhedral convexity
2E Variational inequalities with monotonicity
2G. Consequences for optimization
Chapter 3. Regularity properties of set-valued solution mappings
3A. Set convergence
3B. Continuity of set-valued mappings
3C. Lipschitz continuity of set-valued mappings
3D. Outer Lipschitz continuity
3E. Aubin property, metric regularity and linear openness
3F. Implicit mapping theorems with metric regularity
3G. Strong metric regularity
3H. Calmness and metric subregularity
31. Strong metric subregularity
Chapter 4. Regularity properties through generalized derivatives
4A. Graphical differentiation
4B. Derivative criteria for the Aubin property
4C. Characterization of strong metric subregularity
4D. Applications to parameterized constraint systems
4E. Isolated calmness for variational inequalities
4F. Single-valued Idealizations for variational inequalities
4G. Special nonsmooth inverse function theorems
4H. Results utilizing coderivatives
Chapter 5. Regularity in infinite dimensions
5A. Openness and positively homogeneous mappings
5B. Mappings with closed and convex graphs
5C. Sublinear mappings
5D. The theorems of Lyusternik and Graves
5E. Metric regularity in metric spaces
5V. Strong metric regularity and implicit function theorems
5G. The Bartle-Graves theorem and extensions
Chapter 6. Applications in numerical variational analysis
6A. Radius theorems and conditioning
6B. Constraints and feasibility
6C. Iterative processes for generalized equations
6D. An implicit function theorem for Newton's iteration
6E. Galerkin's method for quadratic minimization
6F. Approximations in optimal control
References
Notation
Index
