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隐函数定理是分析的最主要定理之一，是偏微分方程和数值分析的最基本工具。邓契夫等编著的《隐函数和解映射》在经典框架及其外研究隐函数的本质，主要侧重于研究变分问题解映射的性质。本书自称体系，并将大量散落的材料综合起来，旨在提供一个研究这门学科的参考书籍。第一章以一种学生和本科生微积分的老师新闻乐见的方式讲述经典隐函数定理，以下的章节在难度上逐渐增加，将隐映射看作是一种关联定义的，而非方程定义的。书中讲述了数值分析和优化中的应用。本书是本学科学术上的巨大成果，注定会成为这门学科的一本标准参考书。
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Prelace
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
1E 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
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
3I．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 Iocalizations 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
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