隐函数和解映射 （英文版）

书籍目录

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

作者简介

《隐函数和解映射(英文)》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。《隐函数和解映射(英文)》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。

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