Abstract
The problem of minimizing the energy of a system of \(N\) points on a sphere in \({{\mathbb{R}}^{3}}\), interacting with the potential \(U = \tfrac{1}{{{{r}^{s}}}}\), \(s > 0\), where \(r\) is the Euclidean distance between a pair of points, is considered. A method of projective coordinate descent using a fast calculation of the function and the gradient, as well as a second-order coordinate descent method that rapidly approaches the minimum values known from the literature is proposed.
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This work is supported by the Russian Science Foundation, project no. 16-11-10015.
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Translated by E. Chernokozhin
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Polyak, B.T., Fatkhullin, I.F. Use of Projective Coordinate Descent in the Fekete Problem. Comput. Math. and Math. Phys. 60, 795–807 (2020). https://doi.org/10.1134/S0965542520050127
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DOI: https://doi.org/10.1134/S0965542520050127