title: Using tropical optimization to solve minimax location problems with rectilinear metric on the line
metadata.name: dc.contributor.author
metadata.value: Krivulin, Nikolai K.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Plotnikov, Pavel V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-01-05T17:59:06Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-01-05T17:59:06Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2016-12
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Krivulin N. K., Plotnikov P. V. Using tropical optimization to solve minimax location problems with rectilinear metric on the line. Vestnik of Saint Petersburg University. Series 1. Mathematics. Mechanics. Astronomy, 2016, vol. 3 (61), issue 4, pp. 602–614.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2016.409
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/5900
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: Methods of tropical (idempotent) mathematics are applied to the solution of minimax location problems
  under constraints on the feasible location region. A tropical optimization problem is first considered,
  formulated in terms of a general semifield with idempotent addition. To solve the optimization problem, a
  parameter is introduced to represent the minimum value of the objective function, and then the problem
  is reduced to a parametrized system of inequalities. The parameter is evaluated using existence conditions
  for solutions of the system, whereas the solutions of the system for the obtained value of the parameter are
  taken as the solutions of the initial optimization problem. Then, a minimax location problem is formulated
  to locate a single facility on a line segment in the plane with rectilinear metric. When no constraints are
  imposed, this problem, which is also known as the Rawls problem or the messenger boy problem, has known
  geometric and algebraic solutions. For the location problems, where the location region is restricted to a
  line segment, a new solution is obtained, based on the representation of the problems in the form of the
  tropical optimization problem considered above. Explicit solutions of the problems for various positions
  of the line are given both in terms of tropical mathematics and in the standard form. Refs 16.
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. Series 1. Mathematics. Mechanics. Astronomy;Vol. 3 (61); Issue 4
metadata.lang: -
metadata.name: dc.subject
metadata.value: tropical optimization
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: idempotent semifield
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: rectilinear metric
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: Rawls location problem with constraints
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Using tropical optimization to solve minimax location problems with rectilinear metric on the line
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 09-Krivulin.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/5900/1/09-Krivulin.pdf
resources.format: Adobe PDF
resources.size: 262,44 kB