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Semismooth and Smoothing Newton Methods

  • Book
  • Feb 2025

Overview

Authors:
  1. Liqun Qi

    1. Hong Kong Polytechnic University Dept. Applied Mathematics, Hung Hom, Kowloon, Hong Kong

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  2. Defeng Sun

    1. for Industrial Mathematics, National University of Singapore Dept. of Mathematics & Center, Singapore, Singapore

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  3. Michael Ulbrich

    1. Fakultät für Mathematik, M1, Technische Universität München, Garching bei München, Germany

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  • Presents a comprehensive treatment of the development of the generalized Newton method for solving nonsmooth equations and related problems with applications in optimization
  • Systematic treatment of subject

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About this book

Since its introduction by Isaac Newton (1669) and Joseph Raphson (1690) more than three hundred years ago, Newton's method or the Newton-Raphson method has become the most important technique for solving the system of smooth algebraic equations. Despite its simple structure, Newton's method possesses a fast local convergence rate - superlinear or quadratic. This outstanding feature of Newton's method leads to numerous extensions in the literature. Most of these extensions focus on systems of smooth equations. Since the 1980s, researchers the fields of optimization and numerical analysis have been working on extending Newton's method to non-differentiable system of algebraic equations.

This book presents a comprehensive treatment of the development of the generalized Newton method for solving nonsmooth equations and related problems which grow out of science, engineering, economics and business and sheds light on further investigations of this fascinating topic oriented towards applications in optimization. Semismooth analysis, which form the backbone of further developments, is developed in Chapter 1. Topics then unfold systematically, with apposite illustrations and examples.

Graduate students and researchers in this area will find the book useful.

Authors and Affiliations

  • Hong Kong Polytechnic University Dept. Applied Mathematics, Hung Hom, Kowloon, Hong Kong

    Liqun Qi

  • for Industrial Mathematics, National University of Singapore Dept. of Mathematics & Center, Singapore, Singapore

    Defeng Sun

  • Fakultät für Mathematik, M1, Technische Universität München, Garching bei München, Germany

    Michael Ulbrich

Bibliographic Information

  • Book Title: Semismooth and Smoothing Newton Methods

  • Authors: Liqun Qi, Defeng Sun, Michael Ulbrich

  • Series Title: Springer Series in Operations Research and Financial Engineering

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media, LLC, part of Springer Nature 2025

  • Hardcover ISBN: 978-0-387-79149-4Due: 01 March 2025

  • eBook ISBN: 978-0-387-79150-0Due: 01 March 2025

  • Series ISSN: 1431-8598

  • Series E-ISSN: 2197-1773

  • Edition Number: 1

  • Number of Pages: 250

  • Number of Illustrations: 20 b/w illustrations

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