Use of Projective Coordinate Descent in the Fekete Problem

Autor: Ilyas Fatkhullin, Boris T. Polyak
Rok vydání: 2020
Předmět:
Zdroj: Computational Mathematics and Mathematical Physics. 60:795-807
ISSN: 1555-6662
0965-5425
DOI: 10.1134/s0965542520050127
Popis: 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.
Databáze: OpenAIRE
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