Journal of Convex Analysis 18 (2011), No. 3, 687--698
Copyright Heldermann Verlag 2011
On the Infimum of a Quasiconvex Function over an Intersection. Application to the Distance Function
Juan-Enrique Martínez Legaz
Dep. d'Economia i d'Història Econòmica, Universitat Autònoma de Barcelona, 08193 Bellaterra - Barcelona, Spain
JuanEnrique.Martinez.Legaz@uab.es
Antonio Martinón
Dep. de Análisis Matemático, Universidad de La Laguna, 38271 La Laguna - Tenerife, Spain
anmarce@ull.es
[Abstract-pdf]
We give sufficient conditions for the infimum of a quasiconvex function $f$ over the intersection $\bigcap_{i\in I}R_{i}$ to agree with the supremum of the infima of $f$ over the $R_{i}$'s. We apply these results to the distance function in a normed space.
Keywords: Quasiconvex functions, distance to the intersection.
MSC: 54E35; 26-99
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