Solving a Generalized Heron Problem by means of Convex Analysis
Optimization and Control
2010-11-16 v1
Abstract
The classical Heron problem states: \emph{on a given straight line in the plane, find a point such that the sum of the distances from to the given points and is minimal}. This problem can be solved using standard geometry or differential calculus. In the light of modern convex analysis, we are able to investigate more general versions of this problem. In this paper we propose and solve the following problem: on a given nonempty closed convex subset of , find a point such that the sum of the distances from that point to given nonempty closed convex subsets of is minimal.
Cite
@article{arxiv.1011.3242,
title = {Solving a Generalized Heron Problem by means of Convex Analysis},
author = {Boris Mordukhovich and Nguyen Mau Nam and Juan Salinas},
journal= {arXiv preprint arXiv:1011.3242},
year = {2010}
}