On the Infimum of a Quasiconvex Function over an Intersection. Application to the Distance Function

Juan-Enrique Martínez Legaz; Antonio Martinón

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

Quasiconvex functions
distance to the intersection

Mathematics Subject Classification

54E35; 26-99

Suggested citation

J.-E. Martínez Legaz, A. Martinón. “On the Infimum of a Quasiconvex Function over an Intersection. Application to the Distance Function.” Journal of Convex Analysis 18 (2011), No. 3, 687–698.