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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 5, Pages 815–827 (Mi zvmmf11076)  

Use of projective coordinate descent in the Fekete problem

B. T. Polyaka, I. F. Fatkhullinb

a Institute of Control Sciences, Russian Academy of Sciences, Moscow, 117342 Russia
b Moscow Institute of Physics and Technology, Dolgoprudny, Moscow oblast, 141700 Russia

Abstract: The problem of minimizing the energy of a system of $N$ points on a sphere in $\mathbb{R}^3$, interacting with the potential $U=\frac1{{r}^{s}}$, $s>0$ , 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.

Key words: energy minimization on a sphere, Fekete problem, Thomson problem, projective coordinate descent.

Funding Agency Grant Number
Russian Science Foundation 16-11-10015
This work is supported by the Russian Science Foundation, project no. 16-11-10015.


DOI: https://doi.org/10.31857/S0044466920050129


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:5, 795–807

Bibliographic databases:

UDC: 519.85
Received: 21.09.2019
Revised: 21.09.2019
Accepted:14.01.2020

Citation: B. T. Polyak, I. F. Fatkhullin, “Use of projective coordinate descent in the Fekete problem”, Zh. Vychisl. Mat. Mat. Fiz., 60:5 (2020), 815–827; Comput. Math. Math. Phys., 60:5 (2020), 795–807

Citation in format AMSBIB
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\paper Use of projective coordinate descent in the Fekete problem
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\vol 60
\issue 5
\pages 815--827
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\crossref{https://doi.org/10.31857/S0044466920050129}
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\jour Comput. Math. Math. Phys.
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\vol 60
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\pages 795--807
\crossref{https://doi.org/10.1134/S0965542520050127}
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