Finite-Dimensional Variational Inequalities and Complementarity Problems - Springer Series in Operations Research and Financial Engineering

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Finite-Dimensional Variational Inequalities and Complementarity Problems

Finite-Dimensional Variational Inequalities and Complementarity Problems - Springer Series in Operations Research and Financial Engineering

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5.00 (1 Ratings by Goodreads)
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Published: 17 September, 2011
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Description

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).
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Type Book
ISBN13 9781441930644
ISBN10 1441930647
Number Of Pages 704
Item Weight 1000 g
Publisher / Reseller Springer-Verlag New York Inc.
Format paperback
Edition Softcover reprint of the original 1st ed. 2003
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Media Reviews

Aus den Rezensionen: "... Die behandelten Aufgabenstellungen lassen sich rasch prazisieren. ... 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 fur fortgeschrittene Studenten, einschliesslich Doktoranden ... geeignet ... Es ist ein grossartiges Werk, das sich uber langere Zeit hinweg zur Standardreferenz etablieren wird." (J. Gwinner, in: Jahresbericht der Deutschen Mathematiker-Vereinigung, 2006, Vol. 108, Issue 3, S. 16 ff.)

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Author's Bio

 

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

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