Finite-Dimensional Variational Inequalities and Complementarity Problems

Francisco Facchinei, Jong-Shi Pang (Autoren)

Buch | Softcover

704 Seiten

2011 | Softcover reprint of the original 1st ed. 2003
Springer-Verlag New York Inc.
978-1-4419-3064-4 (ISBN)

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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).

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

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.

Reihe/Serie	Springer Series in Operations Research and Financial Engineering
Zusatzinfo	3 Illustrations, black and white; 704 p. 3 illus.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Informatik ► Weitere Themen ► CAD-Programme
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik
	Wirtschaft ► Betriebswirtschaft / Management ► Unternehmensführung / Management
ISBN-10	1-4419-3064-7 / 1441930647
ISBN-13	978-1-4419-3064-4 / 9781441930644
Zustand	Neuware