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Finite-Dimensional Variational Inequalities and Complementarity Problems / Edition 1

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Overview

This comprehensive book presents a rigorous and state-of-the-art treatment of variational inequalities and complementarity problems in finite dimensions. This class of mathematical programming problems provides a powerful framework for the unified analysis and development of efficient solution algorithms for a wide range of equilibrium problems in economics, engineering, finance, and applied sciences. New research material and recent results, not otherwise easily accessible, are presented in a self-contained and consistent manner. The book is published in two volumes, with the first volume concentrating on the basic theory and the second on iterative algorithms. Both volumes contain abundant exercises and feature extensive bibliographies. Written with a wide range of readers in mind, including graduate students and researchers in applied mathematics, optimization, and operations research as well as computational economists and engineers, this book will be an enduring reference on the subject and provide the foundation for its sustained growth.

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Editorial Reviews

From the Publisher

From the reviews:

"The first volume consists of the first six chapters, which present the basic theory of VIs and CPs. ... Besides the main text, each chapter contains (a) an extensive set of exercises … and (b) a set of notes and comments that document historical accounts, give the sources for the results in the main text, and provide discussions and references on related topics and extensions. … The book is written very well and is an important contribution to the fields of VIs and CPs." (Jürgen Guddat, Zentralblatt MATH, Vol. 1062 (13), 2005)

"This … monograph presents a comprehensive and state-of-the-art treatment of variational inequalities (VI) in finite dimensions. … The presentation is clear, consistent, and essentially self-contained. The book contains a lot of new research material and recent results … . The discussion of related literature is a mine both for researchers and new comers … . the book is of high value not only for specialists, but for a wide range of readers … . It may recommended both for researchers and advanced students … ." (Diethard Klatte, OR-News, March, 2005)

"Represents a successful endeavour resulting in a valuable source for researchers, advanced graduates, and for practitioners with an applied mathematics background. It will also well augment a library’s section on variational inequalities (VIs) and complementarity problems (CPs). … merits of the book include the motivation and guideline at the beginning of each chapter, a variety of exercises, further discussion in the form of notes and comments and pointers to the relevant literature at the end of each chapter, and a comprehensive reference list … ." (M Hintermueller, Journal of the Operational Research Society, Vol. 55 (9), 2004)

"This … monograph, written for novice and expert researchers and advanced graduate students in a wide range of disciplines, presents a comprehensive, state-of-the-art treatment of the finite-dimensional variational inequality and complementarity problem … . It includes every major aspect of VI/CP … including novel application domains." (Quarterly of Applied Mathematics, Vol. LXI (3), 2003)

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Product Details

Meet the Author

Jong-Shi Pang was awarded the 2003 Dantzig Prize, the worlds top prize in the area of Mathematical Programming.

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Table of Contents

Introduction
• Solution Analysis I
• Solution Analysis II
• The Euclidean Projector and Piecewise Functions
• Sensitivity and Stability
• Theory of Error Bounds
• Bibliography
• Index

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