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:	9781441930644
Publisher:	Springer New York
Publication date:	09/17/2011
Series:	Springer Series in Operations Research and Financial Engineering
Edition description:	Softcover reprint of the original 1st ed. 2003
Pages:	704
Product dimensions:	6.10(w) x 9.25(h) x 0.06(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.

Editorial Reviews

Aus den Rezensionen:

"… Die behandelten Aufgabenstellungen lassen sich rasch präzisieren. … Vorbildlich ist die Organisation des Stoffes: … jedes Kapitel mit einer Einleitung beginnend, die klar die abgehandelten Themen benennt … sowie zu jedem Kapitel abschließend ein Abschnitt ‘Notes and Comments‘, der den Stoff einordnet und die Quellen zu den wichtigsten Ergebnissen nennt … So spricht dieses Werk nicht nur den Fachmann an. Es ist gleichermaßen bestens für fortgeschrittene Studenten, einschließlich Doktoranden … geeignet … Es ist ein großartiges Werk, das sich über längere Zeit hinweg zur Standardreferenz etablieren wird."

(J. Gwinner, in: Jahresbericht der Deutschen Mathematiker-Vereinigung, 2006, Vol. 108, Issue 3, S. 16 ff.)

From the Publisher