Finite-Dimensional Variational Inequalities and Complementarity Problems

• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Άλλοι συγγραφείς: Facchinei, Francisco (Επιμελητής έκδοσης), Pang, Jong-Shi (Επιμελητής έκδοσης)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: New York, NY : Springer New York, 2003.
• Σειρά: Springer Series in Operations Research and Financial Engineering,
• Θέματα: Mathematics.; Operations research.; Decision making.; Game theory.; Mathematical optimization.; Management science.; Applied mathematics.; Engineering mathematics.; Operations Research, Management Science.; Optimization.; Operation Research/Decision Theory.; Game Theory, Economics, Social and Behav. Sciences.; Appl.Mathematics/Computational Methods of Engineering.

 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). 

 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.