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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
Usually ships in 15 to 20 working days
Ref
99-15
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