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Finite-Dimensional Variational Inequalities and Complementarity Problems

  • Francisco Facchinei
  • Jong-Shi Pang

Table of contents

  1. Front Matter
    Pages I-XXXIII
  2. Pages 891-988
  3. Back Matter
    Pages II-1-II-57

About this book

Introduction

The ?nite-dimensional nonlinear complementarity problem (NCP) is a s- tem of ?nitely many nonlinear inequalities in ?nitely 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 in ?nite dimensions, provides a powerful framework for the modeling of equilibria of many kinds, and exhibits a natural link between smooth and nonsmooth mathematics. The ?nite-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 ?nite-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 ?eld of mathematical programming. The - velopments include a rich mathematical theory, a host of e?ective 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 bene?ted 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, ?nancial, and spatial).

Keywords

algorithm algorithms mathematical programming operations research optimization programming

Editors and affiliations

  • Francisco Facchinei
    • 1
  • Jong-Shi Pang
    • 2
  1. 1.Dipartimento di Informatica e SistemisticaUniversità di Roma “La Sapienza”RomeItaly
  2. 2.Department of Mathematical SciencesThe Johns Hopkins UniversityBaltimoreUSA

Bibliographic information

  • DOI https://doi.org/10.1007/b97544
  • Copyright Information Springer-Verlag New York, Inc. 2003
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-95581-0
  • Online ISBN 978-0-387-21815-1
  • Series Print ISSN 1431-8598
  • Buy this book on publisher's site