[Opt-net] new book

[Asen Dontchev]

    Implicit Functions and Solution Mappings

A View from Variational Analysis
Series: Springer Monographs in Mathematics 
<http://www.springer.com/series/3733>
*Dontchev*, Asen L., *Rockafellar*, R. Tyrrell
2009, XII, 376 p. 12 illus., Hardcover
ISBN: 978-0-387-87820-1

The implicit function theorem is one of the most important theorems in 
analysis and its many variants are basic tools in partial differential 
equations and numerical analysis. This book treats the implicit function 
paradigm in the classical framework and beyond, focusing largely on 
properties of solution mappings of variational problems.

The purpose of this self-contained work is to provide a reference on the 
topic and to provide a unified collection of a number of results which 
are currently scattered throughout the literature. The first chapter of 
the book treats the classical implicit function theorem in a way that 
will be useful for students and teachers of undergraduate calculus. The 
remaining part becomes gradually more advanced, and considers implicit 
mappings defined by relations other than equations, e.g., variational 
problems. Applications to numerical analysis and optimization are also 
provided.

This valuable book is a major achievement and is sure to become a 
standard reference on the topic.

Written for:

Graduate students, researchers