A Note on Weighted Fermat Problem in Lp Space

Abstract

In this paper, we begin by introducing a well-known geometry concept: the Fermat point in a triangle. Then, we generalize the problem and propose an iterative algorithm based on gradient descent to the weighted form in Lp space. We also build specific solutions to some special norms: one, two and infinity. We show that the solution may not be unique in norm-one and infinity. Finally, we provide our qualitative results in the PASCAL-based program.

arXiv comment8 pages, 4 figures, 3 tables