隐函数和解映射（英文版）
作者：（美）邓契夫 著
出版时间：2013年版
内容简介
Setting up equations and solving them has long been so important that， in popular imagination， it has virtually come to describe what mathematical analysis and its applications are all about. A central issue in the subject is whether the solution to an equation involving parameters may be viewed as a function of those parameters， and if so， what properties that function might have. This is addressed by the classical theory ofimplicit functions， which began with single real variables and progressed through multiple variables to equations in infinite dimensions， such as equations associated with inLegral and differential operators.
目录
Preface
Acknowledgements
Chapter 1. Functions defined implicitly by equations
1A. The classical inverse function theorem
1B. The classical implicit function theorem
1C. Calmness
1D. Lipschitz continuity
1E. Lipschitz invertibility from approximations
1F. Selections of multi-valued inverses
1G. 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
2F. Variational inequalities with monotonicity
2G. Consequences t'or 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
3L Strong metric subregularity
Chapter 4. Regularity properties through generalized derivatives
4A. Graphical differentiation
4B. Derivative crkeria 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 localizations 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
5F. 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
