TitleFinite-Dimensional Variational Inequalities and Complementarity Problems [electronic resource] / edited by Francisco Facchinei, Jong-Shi Pang
ImprintNew York, NY : Springer New York, 2003
Connect tohttp://dx.doi.org/10.1007/b97544
Descript 704 p. 3 illus. online resource

SUMMARY

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)


CONTENT

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


SUBJECT

  1. Mathematics
  2. Operations research
  3. Decision making
  4. Game theory
  5. Mathematical optimization
  6. Management science
  7. Applied mathematics
  8. Engineering mathematics
  9. Mathematics
  10. Operations Research
  11. Management Science
  12. Optimization
  13. Operation Research/Decision Theory
  14. Game Theory
  15. Economics
  16. Social and Behav. Sciences
  17. Appl.Mathematics/Computational Methods of Engineering