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Link to original content: https://link.springer.com/doi/10.1007/978-1-4614-4340-7
Introduction to Piecewise Differentiable Equations | SpringerLink
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Introduction to Piecewise Differentiable Equations

  • Book
  • © 2012

Overview

Authors:
  1. Stefan Scholtes

    1. Judge Business School, Dept. Engineering, University of Cambridge, Cambridge, United Kingdom

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  • 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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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.

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Table of contents (5 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Sample Problems for Nonsmooth Equations

    • Stefan Scholtes
    Pages 1-12

  3. Piecewise Affine Functions

    • Stefan Scholtes
    Pages 13-63

  4. Elements from Nonsmooth Analysis

    • Stefan Scholtes
    Pages 65-90

  5. Piecewise Differentiable Functions

    • Stefan Scholtes
    Pages 91-111

  6. Sample Applications

    • Stefan Scholtes
    Pages 113-125

  7. Back Matter

    Pages 127-133
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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

  • Judge Business School, Dept. Engineering, University of Cambridge, Cambridge, United Kingdom

    Stefan Scholtes

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