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Semismooth and Smoothing Newton Methods

Buch | Hardcover
250 Seiten
2025 | 1st ed. 2025
Springer-Verlag New York Inc.
978-0-387-79149-4 (ISBN)
65,91 inkl. MwSt
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.

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.

Erscheint lt. Verlag 28.6.2025
Reihe/Serie Springer Series in Operations Research and Financial Engineering
Springer Series in Operations Research and Financial Engineering
Zusatzinfo 20 Illustrations, black and white; 250 p. 20 illus.
Verlagsort New York, NY
Sprache englisch
Maße 155 x 235 mm
Themenwelt Mathematik / Informatik Mathematik Analysis
Mathematik / Informatik Mathematik Angewandte Mathematik
Mathematik / Informatik Mathematik Finanz- / Wirtschaftsmathematik
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Wirtschaft Betriebswirtschaft / Management
ISBN-10 0-387-79149-3 / 0387791493
ISBN-13 978-0-387-79149-4 / 9780387791494
Zustand Neuware
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