Francisco Facchinei, Jong-Shi Pang

Finite-Dimensional Variational Inequalities and Complementarity Problems

• Broschiertes Buch

Produktbeschreibung

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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Produktdetails

• Springer Series in Operations Research and Financial Engineering
• Verlag: Springer / Springer New York / Springer, Berlin
• Artikelnr. des Verlages: 978-1-4419-3064-4
• Softcover reprint of the original 1st ed. 2003
• Seitenzahl: 704
• Erscheinungstermin: 17. September 2011
• Englisch
• Abmessung: 235mm x 155mm x 38mm
• Gewicht: 1058g
• ISBN-13: 9781441930644
• ISBN-10: 1441930647
• Artikelnr.: 32181545

Autorenporträt

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

Inhaltsangabe

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.

Rezensionen

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 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)