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Generalized Convexity and Generalized Monotonicity
. Ed(S): Hadjisavvas, Nicolas; Martinez-Legaz, Juan E.; Penot, Jean-Paul
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Description for Generalized Convexity and Generalized Monotonicity
Paperback. 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. Editor(s): Hadjisavvas, Nicolas; Martinez-Legaz, Juan E.; Penot, Jean-Paul. Series: Lecture Notes in Economics and Mathematical Systems. Num Pages: 419 pages, 1 black & white illustrations, 1 colour illustrations, biography. BIC Classification: PBK; PBU. Category: (P) Professional & Vocational. Dimension: 234 x 156 x 22. Weight in Grams: 597.
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: ... Read more
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: ... Read more
Product Details
Format
Paperback
Publication date
2001
Publisher
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG Germany
Number of pages
419
Condition
New
Series
Lecture Notes in Economics and Mathematical Systems
Number of Pages
410
Place of Publication
Berlin, Germany
ISBN
9783540418061
SKU
V9783540418061
Shipping Time
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Ref
99-15
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