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The classical Heron problem states: \emph{on a given straight line in theplane, find a point $C$ such that the sum of the distances from $C$ to thegiven points $A$ and $B$ is minimal}. This problem can be solved using standardgeometry or differential calculus. In the light of modern convex analysis, weare able to investigate more general versions of this problem. In this paper wepropose and solve the following problem: on a given nonempty closed convexsubset of $\R^s$, find a point such that the sum of the distances from thatpoint to $n$ given nonempty closed convex subsets of $\R^s$ is minimal.

Solving a Generalized Heron Problem by means of Convex Analysis