© 2012

Introduction to Piecewise Differentiable Equations


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



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.


Bouligand derivative NonSmooth Equations Polyhedral theory affine functions piecewise differentiable function

Authors and affiliations

  1. 1.Judge Business School, Dept. EngineeringUniversity of CambridgeCambridgeUnited Kingdom

Bibliographic information

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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)