This article is cited in 2 papers

Mathematics

A variant of a metric for unbounded convex sets

P. D. Lebedev, V. N. Ushakov

Institute of Mathematics and Mechanics of the Russian Academy of Sciences (Ural branch)

Abstract: Convex analysis methods are used for the construction of distance function between closed (un­bounded in common case) sets of Euclidean space. It is shown that the distance satisfies all properties of metric. It is proved that this distance is invariant under motion of the sets in space. This metric space is proved to be complete.

Keywords: Hausdorff distance, metric, convex set, recessive cone.

UDC: 514.17

Received: 18.12.2012