title: Solution of mathematical programming problems using methods of tropical optimization
metadata.name: dc.contributor.author
metadata.value: Krivulin, Nikolai K.
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Romanovsky, Joseph V.
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2017-09-20T13:42:45Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2017-09-20T13:42:45Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2017-09
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Krivulin N.K., Romanovsky J.V. Solution of mathematical programming problems using methods of tropical optimization. Vestnik SPbSU. Mathematics. Mechanics. Astronomy, 2017, vol. 4 (62), issue 3, pp. 448–458.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: 10.21638/11701/spbu01.2017.307
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/7147
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: A class of mathematical programming problems, which includes linear and non-linear programming
  problems of a particular form is considered. First, a linear programming problem is examined and the
  possibility to derive a direct complete solution of the problem, which does not use known iterative
  computational procedures and algorithms of linear programming, such as the simplex algorithm is
  investigated. A direct solution of the problem with a reduced set of constraints and of the minimal
  dimension is given, and it is shown that, as the dimension increases, the derivation of such solutions becomes an extremely hard task, and thus is hardly feasible. Examples of other problems of linear and
  non-linear programming, which can be obtained by isomorphic transformations of the problem considered
  above are presented. Furthermore, an overview of main definitions and preliminary results of tropical
  mathematics, which are necessary in the subsequent description and application of methods of tropical
  mathematics is given. A tropical optimization problem is formulated, and direct complete solutions for
  the problem and its special cases are described. The above problems of linear and non-linear programming
  reduce to the tropical optimization problem, which provides a direct complete solution to the former
  problems in terms of tropical mathematics. For the linear programming problem with a reduced set of
  constraints a representation of the solution in the usual mathematical terms is demonstrated. Refs 17.
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 4 (62); Issue 3
metadata.lang: -
metadata.name: dc.subject
metadata.value: mathematical programming
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: linear programming
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: tropical mathematics
metadata.lang: en_GB
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.title
metadata.value: Solution of mathematical programming problems using methods of tropical optimization
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 07-Krivulin.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/7147/1/07-Krivulin.pdf
resources.format: Adobe PDF
resources.size: 282,19 kB