#### Document Type

Technical Report

#### Abstract

The classical Heron problem states: on a given straight line in the plane, find a point C such that the sum of the distances from C to the given points A and B 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 IR!, find a point such that the sum of the distances from that point to n given nonempty closed convex subsets of JR• is minimal.

#### Number in Series

2010.13

#### Disciplines

Applied Mathematics | Mathematics

#### Recommended Citation

Mordukhovich, Boris S.; Nam, Nguyen Mau; and Salinas, Juan Jr, "Solving a Generalized Heron Problem by Means of Convex Analysis" (2010). *Mathematics Research Reports*. 80.

https://digitalcommons.wayne.edu/math_reports/80

## Comments

This research was partially supported by the US National Science Foundation under grants DMS-0603846 and DMS-1007132 and by the Australian Research Council under grant DP-12092508.