Authors:
- Introduces the theory of piecewise differentiable functions with an emphasis on piecewise differentiable equations Illustrates the relevance of the study via two sample problems
Part of the book series: SpringerBriefs in Optimization (BRIEFSOPTI)
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Table of contents (5 chapters)
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Front Matter
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Back Matter
About this book
This brief provides an elementary introduction to the theory of piecewise differentiable functions with an emphasis on differentiable equations. In the first chapter, two sample problems are used to motivate the study of this theory. The presentation is then developed using two basic tools for the analysis of piecewise differentiable functions: the Bouligand derivative as the nonsmooth analogue of the classical derivative concept and the theory of piecewise affine functions as the combinatorial tool for the study of this approximation function. In the end, the results are combined to develop inverse and implicit function theorems for piecewise differentiable equations.
This Introduction to Piecewise Differentiable Equations will serve graduate students and researchers alike. The reader is assumed to be familiar with basic mathematical analysis and to have some familiarity with polyhedral theory.
Reviews
From the reviews:
“The book is nicely written with a lucid yet rigorous presentation of the mathematical concepts and constructions involved. It does not require prerequisites far beyond multivariable calculus and basic linear algebra … . This book is a welcome addition to the bookshelf of anyone who is interested in polyhedral combinatorics and nonsmooth analysis, and applications to sensitivity analysis of variational inequalities.” (Asen L. Dontchev, Mathematical Reviews, January, 2013)Authors and Affiliations
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Judge Business School, Dept. Engineering, University of Cambridge, Cambridge, United Kingdom
Stefan Scholtes
Bibliographic Information
Book Title: Introduction to Piecewise Differentiable Equations
Authors: Stefan Scholtes
Series Title: SpringerBriefs in Optimization
DOI: https://doi.org/10.1007/978-1-4614-4340-7
Publisher: Springer New York, NY
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Stefan Scholtes 2012
Softcover ISBN: 978-1-4614-4339-1Published: 01 August 2012
eBook ISBN: 978-1-4614-4340-7Published: 01 August 2012
Series ISSN: 2190-8354
Series E-ISSN: 2191-575X
Edition Number: 1
Number of Pages: X, 133
Topics: Analysis, Functions of a Complex Variable, Calculus of Variations and Optimal Control; Optimization