Semismooth and Smoothing Newton Methods by Liqun QiSemismooth and Smoothing Newton Methods by Liqun Qi

Semismooth and Smoothing Newton Methods

byLiqun Qi

Hardcover | January 22, 2018

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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.

Title:Semismooth and Smoothing Newton MethodsFormat:HardcoverDimensions:238 pagesPublished:January 22, 2018Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387791493

ISBN - 13:9780387791494

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Table of Contents

Preface.- Smooth Analysis.- Semismooth Newton Methods.- Smoothing Newton Methods.- Complementarity Problems and Variational Inequalities.- Semismooth Integration Functions.- Semismooth Matrix Functions.- Infinite Dimensional Spaces.- Bibliography.- Index.