First Advisor
Mau Nam Nguyen
Date of Award
2016
Document Type
Thesis
Degree Name
Bachelor of Arts (B.A.) in Mathematics and University Honors
Department
Mathematics
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.
Rights
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Persistent Identifier
http://archives.pdx.edu/ds/psu/17431
Recommended Citation
Lawrence, Nathan, "Convex and Nonconvex Optimization Techniques for the Constrained Fermat-Torricelli Problem" (2016). University Honors Theses. Paper 317.
https://doi.org/10.15760/honors.319