title: Multi-objective Optimization Approach to Malfatti's Problem
metadata.name: dc.contributor.author
metadata.value: Enkhbat, Rentsen
metadata.lang: -
metadata.name: dc.contributor.author
metadata.value: Battur, Gompil
metadata.lang: -
metadata.name: dc.date.accessioned
metadata.value: 2021-11-26T17:44:14Z
metadata.lang: -
metadata.name: dc.date.available
metadata.value: 2021-11-26T17:44:14Z
metadata.lang: -
metadata.name: dc.date.issued
metadata.value: 2021-10
metadata.lang: -
metadata.name: dc.identifier.citation
metadata.value: Enkhbat R., Battur G. Multi-objective Optimization Approach to Malfatti's Problem. Contributions to Game Theory and Management, XIV, 82-90.
metadata.lang: en_GB
metadata.name: dc.identifier.other
metadata.value: https://doi.org/10.21638/11701/spbu31.2021.07
metadata.lang: -
metadata.name: dc.identifier.uri
metadata.value: http://hdl.handle.net/11701/33689
metadata.lang: -
metadata.name: dc.description.abstract
metadata.value: In this work, we consider the multi-objective optimization problem
  based on the circle packing problem, particularly, extended Malfatti's
  problem (Enkhbat, 2020) with k disks. Malfatti's problem was examined
  for the first time from a view point of global optimization theory and algorithm
  in (Enkhbat, 2016). Also, a game theory approach has been applied
  to Malfatti's problem in (Enkhbat and Battur, 2021). In this paper, we apply
  the the multi-objective optimization approach to the problem. Using the
  weighted sum method, we reduce this problem to optimization problem with
  nonconvex constraints. For solving numerically the weighted sum optimization
  problem, we apply KKT conditions and find Pareto stationary points.
  Also, we estimate upper bounds of the global value of the objective function
  by Lagrange duality. Numerical results are provided.
metadata.lang: en_GB
metadata.name: dc.language.iso
metadata.value: en
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: Contributions to Game Theory and Management;Volume 14
metadata.lang: -
metadata.name: dc.subject
metadata.value: circle packing problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: triangle set
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: k disks
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: multi-objective optimization problem
metadata.lang: en_GB
metadata.name: dc.subject
metadata.value: upper bound
metadata.lang: en_GB
metadata.name: dc.title
metadata.value: Multi-objective Optimization Approach to Malfatti's Problem
metadata.lang: en_GB
metadata.name: dc.type
metadata.value: Article
metadata.lang: en_GB
resources.filename: 82-90.pdf
resources.url: https://dspace.spbu.ru/bitstream/11701/33689/1/82-90.pdf
resources.format: Adobe PDF
resources.size: 467,33 kB