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Softcover/Paperback. Condizione: Gut. 410 Seiten. Laminiertes ehem. Bibliotheksexemplar mit Rückensignatur und Stempeln. Gut erhalten. 9783540418061 Sprache: Englisch Gewicht in Gramm: 1200.

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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - A famous saying (due toHerriot)definescultureas 'what remainswhen everythingisforgotten '. One couldparaphrase thisdefinitionin statingthat generalizedconvexity iswhat remainswhen convexity has been dropped . Of course, oneexpectsthatsome convexityfeaturesremain.For functions, convexity ofepigraphs(what is above thegraph) is a simplebut strong assumption.It leads tobeautifulpropertiesand to a field initselfcalled convex analysis. In several models, convexity is not presentandintroducing genuine convexityassumptionswouldnotberealistic. A simple extensionof thenotionof convexity consists in requiringthatthe sublevel sets ofthe functionsare convex (recall thata sublevel set offunction a is theportionof thesourcespaceon which thefunctiontakesvalues below a certainlevel).Its first use is usuallyattributed to deFinetti,in 1949. This propertydefinesthe class ofquasiconvexfunctions, which is much larger thanthe class of convex functions: a non decreasingor nonincreasingone variablefunctionis quasiconvex ,as well asanyone-variable functionwhich is nonincreasingon someinterval(-00,a] or(-00,a) and nondecreasingon its complement.Many otherclasses ofgeneralizedconvexfunctionshave been introduced ,often fortheneeds ofvariousapplications: algorithms ,economics, engineering ,management science,multicriteria optimization ,optimalcontrol, statistics .Thus,theyplay animportantrole in severalappliedsciences . A monotonemappingF from aHilbertspace to itself is a mappingfor which the angle between F(x) - F(y) and x- y isacutefor anyx, y. It is well-known thatthegradientof a differentiable convexfunctionis monotone.The class of monotonemappings(and theclass ofmultivaluedmonotoneoperators) has remarkableproperties.This class has beengeneralizedin various direc tions,withapplicationsto partialdifferentialequations ,variationalinequal ities,complementarity problemsand more generally, equilibriumproblems. The classes ofgeneralizedmonotonemappingsare more or lessrelatedto the classes ofgeneralizedfunctionsvia differentiation or subdifferentiation procedures.They are also link edvia severalothermeans.…

Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - In recent years there is a growing interest in generalized convex fu- tions and generalized monotone mappings among the researchers of - plied mathematics and other sciences. This is due to the fact that mathematical models with these functions are more suitable to describe problems of the real world than models using conventional convex and monotone functions. Generalized convexity and monotonicity are now considered as an independent branch of applied mathematics with a wide range of applications in mechanics, economics, engineering, finance and many others. The present volume contains 20 full length papers which reflect c- rent theoretical studies of generalized convexity and monotonicity, and numerous applications in optimization, variational inequalities, equil- rium problems etc. All these papers were refereed and carefully selected from invited talks and contributed talks that were presented at the 7th International Symposium on Generalized Convexity/Monotonicity held in Hanoi, Vietnam, August 27-31, 2002. This series of Symposia is or- nized by the Working Group on Generalized Convexity (WGGC) every 3 years and aims to promote and disseminate research on the field. The WGGC consists of more than 300 researchers coming from 36 countries.…

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Taschenbuch. Condizione: Neu. Generalized Convexity, Generalized Monotonicity and Applications | Proceedings of the 7th International Symposium on Generalized Convexity and Generalized Monotonicity | Andrew Eberhard (u. a.) | Taschenbuch | Nonconvex Optimization and Its Applications | x | Englisch | 2010 | Springer | EAN 9781441936479 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu.…

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