Finite-Dimensional Variational Inequalities and Complementarity Problems

Springer Science & Business Media, 4 jun. 2007 - 704 pagina's
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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).

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Glossary of Notation
Numbering System xxxiii
Contents of Volume I
Global Methods for Nonsmooth Equations
Solution Analysis I 125
EquationBased Algorithms for CPs
The Euclidean Projector and Piecewise Functions 339
Sensitivity and Stability 419
Algorithms for VIs
Interior and Smoothing Methods
Methods for Monotone Problems
Bibliography for Volume II II1
Solution Analysis II 243
Index of Definitions Results and Algorithms II39
Index of Definitions and Results I51

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Pagina 1271 - Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto, 606-8501, Japan...
Pagina 630 - A complex-valued function on [a, b] is in fiip^fa, &]) [see the definition in (17.31)] if and only if for every e > 0 there is a <5 > 0 such that for all sequences ([ah, &*])"=,! of subintervals of [a, b] for which Z (b, -<*Ľ)<* k=i holds, the inequality holds. That is, / is "absolutely continuous with overlap permitted".

Over de auteur (2007)

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

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