Finite-Dimensional Variational Inequalities and Complementarity Problems / Edition 1

by Francisco Facchinei, Jong-Shi Pang

Overview

Thefinite-dimensional nonlinear complementarity problem (NCP) is a system offinitely many nonlinear inequalities infinitely many nonnegative variables along with a special equation that expresses the complementary relationship between the variables and corresponding inequalities. This complementarity condition is the key feature distinguishing the NCP from a general inequality system, lies at the heart of all constrained optimi- tion problems infinite dimensions, provides a powerful framework for the modeling of equilibria of many kinds, and exhibits a natural link between smooth and nonsmooth mathematics. Thefinite-dimensional variational inequality (VI), which is a generalization of the NCP, provides a broad unifying setting for the study of optimization and equilibrium problems and serves as the main computational framework for the practical solution of a host of continuum problems in the mathematical sciences. The systematic study of the finite-dimensional NCP and VI began in the mid-1960s; in a span of four decades, the subject has developed into a very fruitful discipline in the field of mathematical programming. The - velopments include a rich mathematical theory, a host of effective solution algorithms, a multitude of interesting connections to numerous disciplines, and a wide range of important applications in engineering and economics. As a result of their broad associations, the literature of the VI/CP has benefited from contributions made by mathematicians (pure, applied, and computational), computer scientists, engineers of many kinds (civil, ch- ical, electrical, mechanical, and systems), and economists of diverse exp- tise (agricultural, computational, energy, financial, and spatial).

Product Details

ISBN-13:	9780387955810
Publisher:	Springer New York
Publication date:	02/06/2003
Series:	Springer Series in Operations Research and Financial Engineering
Edition description:	2003
Pages:	704
Product dimensions:	6.10(w) x 9.25(h) x 0.36(d)

About the Author

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

Table of Contents

Local Methods for Nonsmooth Equations* Global Methods for Nonsmooth Equations
• Equation-Based Algorithms for CPs
• Algorithms for VIs
• Interior and Smoothing Methods
• Methods for Monotone Problems
• Bibliography
• Index

Editorial Reviews

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 thefinite-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)

From the Publisher