Journal of Global Optimization

, Volume 72, Issue 4, pp 705–729 | Cite as

A DC programming approach for solving multicast network design problems via the Nesterov smoothing technique

  • W. Geremew
  • N. M. Nam
  • A. Semenov
  • V. Boginski
  • E. Pasiliao


This paper continues our recent effort in applying continuous optimization techniques to study optimal multicast communication networks modeled as bilevel hierarchical clustering problems. Given a finite number of nodes, we consider two different models of multicast networks by identifying a certain number of nodes as cluster centers, and at the same time, locating a particular node that serves as a total center so as to minimize the total transportation cost throughout the network. The fact that the cluster centers and the total center have to be among the given nodes makes these problems discrete optimization problems. Our approach is to reformulate the discrete problems as continuous ones and to apply Nesterov’s smoothing approximation techniques on the Minkowski gauges that are used as distance measures. This approach enables us to propose two implementable DCA-based algorithms for solving the problems. Numerical results and practical applications are provided to illustrate our approach.


DC programming Nesterov’s smoothing techniques Hierarchical clustering Subgradient Fenchel conjugate 

Mathematics Subject Classification

49J52 49J53 90C31 



This material is based upon work supported by the AFRL Mathematical Modeling and Optimization Institute. The authors are grateful to both anonymous referees for their helpful comments that allowed us to improve the original presentation.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • W. Geremew
    • 1
  • N. M. Nam
    • 2
  • A. Semenov
    • 3
  • V. Boginski
    • 4
    • 5
  • E. Pasiliao
    • 6
  1. 1.School of General StudiesStockton UniversityGallowayUSA
  2. 2.Fariborz Maseeh Department of Mathematics and StatisticsPortland State UniversityPortlandUSA
  3. 3.Faculty of Information TechnologyUniversity of JyväskyläJyväskyläFinland
  4. 4.Industrial Engineering & Management SystemsUniversity of Central FloridaOrlandoUSA
  5. 5.Industrial and Systems EngineeringUniversity of FloridaGainesvilleUSA
  6. 6.Munitions Directorate, Air Force Research LaboratoryEglin AFBUSA

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