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
Applied Mathematics | Mathematics
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.