Semismooth and Smoothing Newton Methods

ISBN-13: 9780387791494 / Angielski / Twarda / 2025 / 250 str.

Liqun Qi; Defeng Sun; Michael Ulbrich

Opis

This volume is 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. It looks at further investigations of this topic oriented towards applications in optimization.

Spis treści

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.

O autorze

Michael Ulbrich ist Professor für Mathematische Optimierung an der Technischen Universität München.

Blurb

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.