Draft:Karamardian's anomaly
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In convex analysis, Karamardian's anomaly is an example of a pathological function that is strictly ray-quasiconvex but not quasiconvex.[1] It is defined as follows for all :
To show that it is strictly ray-quasiconvex, the property must hold when and . Since , at least one of and is necessarily , and hence .
To show that it is not quasiconvex, take , and . Then , contradicting that .
References[edit]
- ^ Mayor-Gallego, J. A.; Rufián-Lizana, A.; Ruiz-Canales, P. (1994). "Ray-quasiconvex and f-quasiconvex functions". In Komlósi, S.; Rapcsák, T.; Schaible, S. (eds.). Generalized Convexity. Lecture Notes in Economics and Mathematical Systems, vol 405. Berlin, Heidelberg: Springer. pp. 85–90. doi:10.1007/978-3-642-46802-5_8. ISBN 978-3-642-46802-5.