Introduction to Piecewise Differentiable Equations

  • Stefan Scholtes
Part of the SpringerBriefs in Optimization book series (BRIEFSOPTI)

Table of contents

  1. Front Matter
    Pages i-x
  2. Stefan Scholtes
    Pages 1-12
  3. Stefan Scholtes
    Pages 13-63
  4. Stefan Scholtes
    Pages 65-90
  5. Stefan Scholtes
    Pages 91-111
  6. Stefan Scholtes
    Pages 113-125
  7. Back Matter
    Pages 127-133

About this book

Introduction

​​​​​​​

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.

Keywords

Bouligand derivative NonSmooth Equations Polyhedral theory affine functions piecewise differentiable function

Authors and affiliations

  • Stefan Scholtes
    • 1
  1. 1.Judge Business School, Dept. EngineeringUniversity of CambridgeCambridgeUnited Kingdom

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-4340-7
  • Copyright Information Stefan Scholtes 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-4339-1
  • Online ISBN 978-1-4614-4340-7
  • Series Print ISSN 2190-8354
  • Series Online ISSN 2191-575X
  • About this book