Finite-Dimensional Variational Inequalities and Complementarity Problems

Voorkant
Springer Science & Business Media, 4 jun. 2007 - 704 pagina's
0 Recensies
Reviews worden niet geverifieerd, maar Google checkt wel op nepcontent en verwijdert zulke content als die wordt gevonden.
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).
 

Wat mensen zeggen - Een review schrijven

We hebben geen reviews gevonden op de gebruikelijke plaatsen.

Inhoudsopgave

Glossary of Notation
xxv
Numbering System xxxiii
624
Contents of Volume I
677
Global Methods for Nonsmooth Equations
723
Solution Analysis I 125
789
EquationBased Algorithms for CPs
793
The Euclidean Projector and Piecewise Functions 339
822
Sensitivity and Stability 419
884
Algorithms for VIs
891
Interior and Smoothing Methods
989
Methods for Monotone Problems
1107
Bibliography for Volume II II1
1236
Solution Analysis II 243
1255
Index of Definitions Results and Algorithms II39
1273
Index of Definitions and Results I51
1278
Copyright

Overige edities - Alles bekijken

Veelvoorkomende woorden en zinsdelen

Populaire passages

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.

Bibliografische gegevens