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Item Details
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GENERALIZED CONVEXITY AND GENERALIZED MONOTONICITY
PROCEEDINGS OF THE 6TH INTERNATIONAL SYMPOSIUM ON GENERALIZED CONVEXITY/MONOTONICITY, SAMOS, SEPTEMBER 1999 |
| By: |
Nicolas Hadjisavvas (Editor), Juan E. Martinez-Legaz (Editor), Jean-Paul Penot (Editor) |
| Format: |
Paperback |
| List price:
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£99.99 |
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| ISBN 10: |
3540418067 |
| ISBN 13: |
9783540418061 |
| Publisher: |
SPRINGER-VERLAG BERLIN AND HEIDELBERG GMBH & CO. KG |
| Pub. date: |
10 April, 2001 |
| Edition: |
2001 ed. |
| Series: |
Lecture Notes in Economics and Mathematical Systems 502 |
| Pages: |
410 |
| Description: |
This volume contains a selection of refereed papers presented at the 6th International Symposium on Generalized Convexity/Monotonicity, and aims to review the latest developments in this interdisciplinary field. |
| Synopsis: |
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. |
| Illustrations: |
1 Illustrations, color; 1 Illustrations, black and white; IX, 410 p. 2 |
| Publication: |
Germany |
| Imprint: |
Springer-Verlag Berlin and Heidelberg GmbH & Co. K |
| Returns: |
Returnable |
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