Generalized Convexity and Generalized Monotonicity

Name: Generalized Convexity and Generalized Monotonicity
Brand: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
SKU: 9783540418061
Price: 550.04 RON
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Proceedings of the 6th International Symposium on Generalized Convexity/Monotonicity, Samos, September 1999

Autor: Nicolas Hadjisavvas, Juan E. Martinez-Legaz, Jean-Paul Penot

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Editura: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

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A famous saying (due toHerriot)definescultureas "what remainswhen everythingisforgotten ". One could...

Informații despre carte

Autor

Nicolas Hadjisavvas, Juan E. Martinez-Legaz, Jean-Paul Penot

Limbă

engleză

Legare

Carte - Carte broșată

Publicat

2001

Pagini

410

EAN

9783540418061

ISBN

3540418067

Enbook ID

01563360

Editura

Springer-Verlag Berlin and Heidelberg GmbH & Co. KG

Greutate

1320

Dimensiuni

155 x 235 x 24

Descriere completă

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.

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Generalized Convexity and Generalized Monotonicity

Proceedings of the 6th International Symposium on Generalized Convexity/Monotonicity, Samos, September 1999

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