Date of Award

2016

Document Type

Thesis

Department

Mathematics and Statistics

First Advisor

Mau Nam Nguyen

Subjects

Convex geometry, Mathematical optimization

DOI

10.15760/honors.319

Abstract

The Fermat-Torricelli problem asks for a point that minimizes the sum of the distances to three given points in the plane. This problem was introduced by the French mathematician Fermat in the 17th century and was solved by the Italian mathematician and physicist Torricelli. In this thesis we introduce a constrained version of the Fermat-Torricelli problem in high dimensions that involves distances to a finite number of points with both positive and negative weights. Based on the distance penalty method, Nesterov’s smoothing technique, and optimization techniques for minimizing differences of convex functions, we provide effective algorithms to solve the problem. Attaining numerical results is a work in progress.

Comments

An undergraduate honors thesis submitted in partial fulfillment of the requirements for the degree of Bachelor of Arts in University Honors and Mathematics

Persistent Identifier

http://archives.pdx.edu/ds/psu/17431

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