This was a course project for CS-520 - Computational Methods in Optimization. We investigate the problem of uniformly distributing points onto the surface of a hypersphere (popularly known as the Thomson Problem).

The objective of the Thomson problem is to determine the minimum electrostatic potential energy configuration of N electrons constrained to the surface of a unit sphere that repel each other with a force given by Coulomb's law. This can be easily formulated as an optimization problem of uniformly distributing points onto the surface of a hypersphere.

In this project, we study the effects of using various optimization approaches to solving this problem with high N (data points a.k.a electrons) and high D (dimensions).

For details, please refer to the report:

ThomsonProblem / report / report.pdf

We implemented most of the optimization methods in Matlab and for some of them we used the Poblano Matlab toolbox from https://software.sandia.gov/trac/poblano.

[email protected]

[email protected]