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

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

2012-03-02

arxiv.org/abs/1203.0578v1

Mathematics

Optimization and Control

19 pages, 3 figures

Scientific paper

The generalized Heron problem states: on a closed convex subset of $\Real^d$, find a point such that the sum of the distances from that point to $k$ closed convex subsets of $\Real^d$ is minimal. In a recent issue of this journal, Mordukhovich, Nam, and Salinas pose this problem and solve it with the tools of modern convex analysis. In light of the majorization-minimization principle from computational statistics, we revisit the problem and construct a much faster solution algorithm using only rudimentary techniques from differential calculus.

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