Implicit Functions and Solution Mappings [electronic resource] : A View from Variational Analysis /
Dontchev, Assen L.author.
Rockafellar, R. Tyrrell.author.
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.
Description based upon print version of record.
Includes bibliographical references and index.
Functions Defined Implicitly by Equations -- Implicit Function Theorems for Variational Problems -- Regularity properties of set-valued solution mappings -- Regularity Properties Through Generalized Derivatives -- Regularity in infinite dimensions -- Applications in Numerical Variational Analysis.
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.
Mathematical analysis.
Analysis (Mathematics).
Mathematical optimization.
Engineering economics.
Engineering economy.
Analysis.
Optimization.
Engineering Economics, Organization, Logistics, Marketing.
Springer Monographs in Mathematics