title: On solution of a multidimensional tropical optimization problem using matrix sparsification
metadata.name: dc.contributor.author
metadata.value: Krivulin, Nikolai K.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Sorokin, Vladimir N.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2018-04-26T09:32:38Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2018-04-26T09:32:38Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2018-03
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Krivulin N.K., Sorokin V.N. On solution of a multidimensional tropical optimization problem using matrix sparsification. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2018, vol. 5 (63), issue 1, pp. 91–104.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2018.110
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/9502
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this work a complete solution for a problem of minimizing a function defined on vectors
  with elements from a tropical (idempotent) semifield is proposed. The tropical optimization
  problem under consideration arises, for instance, when one needs to find the best, in the
  sense of Chebyshev metric, approximate solution for tropical vector equations, and occurs in
  various applications, including scheduling, location and decision-making problems. To solve
  the problem, first, the minimum value of the objective function is obtained, a characterization
  of the solution set in the form of a system of inequalities is proposed, and one of the solutions
  is presented. Next, by using a sparsification of the matrix in the problem, an extended set
  of solutions, and then a complete solution in the form of a family of subsets are derived.
  Procedures are described that allow reducing the number of subsets, which one needs to
  examine when constructing the complete solution. It is shown how the complete solution can
  be represented in parametric way in a compact vector form. The solution obtained extends
  known results, which are usually confined to the derivation of one solution and do not allow
  to find the entire solution set. To illustrate the main results of the work numerical examples
  are given for the solution of a problem in the set of three-dimensional vectors.
metadata.lang: en_GB
metadata.name: dc.description.sponsorship
metadata.value: Работа выполнена при финансовой поддержке РГНФ в рамках научного проекта №16-02-00059.
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 5(63); Issue 1
metadata.lang: -
metadata.name: dc.subject
metadata.value: idempotent semifield
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: tropical optimization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Chebyshyov approximation
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: complete solution
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: matrix sparsification
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: On solution of a multidimensional tropical optimization problem using matrix sparsification
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 10-Krivulin.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/9502/1/10-Krivulin.pdf
resources.format: Adobe PDF
resources.size: 337,05 kB