Landbrugsmøderne i Stockholm i 1846 og 1847.

Landbrugsmøderne i Stockholm i 1846 og 1847

Om Saasæd og Radsaaning af Kornarterne.

Om Saasæd og Radsaaning af Kornarterne

Nogle Erfaringer angaaende Jordskokker, Spergel, guul Rundbælle, mørkeblaa Grønkaal, og en ved Tromlen anbragt Forandring.

Nogle Erfaringer angaaende Jordskokker, Spergel, guul Rundbælle, mørkeblaa Grønkaal, og en ved Tromlen anbragt Forandring

Vort Fortids-, Nutids- og Fremtids-Landbrug.

Vort Fortids-, Nutids- og Fremtids-Landbrug

Om Kartofler.

Om Kartofler

Om Sommerstaldfodring.

Om Sommerstaldfodring

Agerdyrkningslæreanstalt paa Skaarupgaard.

Agerdyrkningslæreanstalt paa Skaarupgaard

A Look at the Generalized Heron Problem through the Lens of Majorization-Minimization

In a recent issue of this journal, Mordukhovich et al.\ pose and solve an interesting non-differentiable generalization of the Heron problem in the framework of modern convex analysis. In the generalized Heron problem one is given $k+1$ closed convex sets in \Real^d equipped with its Euclidean norm and asked to find the point in the last set such that the sum of the distances to the first $k$ sets is minimal. In later work the authors generalize the Heron problem even further, relax its convexity assumptions, study its theoretical properties, and pursue subgradient algorithms for solving the convex case. Here, we revisit the original problem solely from the numerical perspective. By exploiting the majorization-minimization (MM) principle of computational statistics and rudimentary techniques from differential calculus, we are able to construct a very fast algorithm for solving the Euclidean version of the generalized Heron problem.Comment: 21 pages, 3 figure