title: Charged balls method for solving some computational geometry problems
metadata.name: dc.contributor.author
metadata.value: Abbasov, Majid E.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-09-20T13:26:36Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-09-20T13:26:36Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Abbasov M.E. Charged balls method for solving some computational geometry problems. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2017, vol. 4 (62), issue 3, pp. 359–369.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2017.301
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/7141
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: The concept of replacing the original stationary optimization problem with a nonstationary mechanical
  system that tends to the position of equilibrium, which coincides with the solution of the initial problem,
  allows us to build effective numerical algorithms. First, differential equations of movement should be
  derived. After that we can get to the difference scheme and thus define iterative computational algorithm. There is a wide class of optimization methods built that way. One of the most known representatives of
  this class is heavy ball method. Such type of algorithms always have parameters which highly affect the
  rate of convergence.
  In this paper we propose and investigate charged balls method which is the other representative of
  this class. It is a new effective optimization method, that allows to solve some computational geometry
  problems. We consider the problem of orthogonal projection of a point onto a convex closed set with
  smooth boundary, and the problem of finding the minimum distance between two such sets. Theorems of
  convergence and estimates for the rate of convergence are obtained. Numerical examples illustrating the
  work of the proposed algorithms are given. Refs 8. Tables 2.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РФФИ (грант №16-31-00056 мол_а).
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: ru
metadata.lang: en_GB
metadata.name: dc.publisher
metadata.value: St Petersburg State University
metadata.lang: en_GB
metadata.name: dc.relation.ispartofseries
metadata.value: Vestnik of St Petersburg University. Mathematics. Mechanics. Astronomy;Volume 4 (62); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: convex optimization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: computational geometry
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: minimal distance
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: charged balls method
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Charged balls method for solving some computational geometry problems
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 01-Abbasov.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/7141/1/01-Abbasov.pdf
resources.format: Adobe PDF
resources.size: 277,43 kB