Interaction energy minimization, symmetry, and optimization methods

Josiah Park
Texas A&M University - College Station

Structured geometric point sets play important roles in coding theory, mathematical biology, computational chemistry, wireless communications, compressed sensing, and `big data' applications due to their often desirable statistical properties for measurement and transmission. I'll describe in this talk some research which investigates numerical phenomena related to interaction energy minimization, detailing several results on continuous `probabilistic' energies. In addition I'll talk about some experiments using parallelized computation and optimization methods like trust-region conjugate gradient to numerically minimize energy. Parts of the talk are represented by collaborations with D. Bilyk, A. Glazyrin, R. Matzke, C. Saltijeral, O. Vlasiuk, and M. Zhong.

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