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

Author

Listed:
  • W. Geremew

    (Stockton University)

  • N. M. Nam

    (Portland State University)

  • A. Semenov

    (University of Jyväskylä)

  • V. Boginski

    (University of Central Florida
    University of Florida)

  • E. Pasiliao

    (Munitions Directorate, Air Force Research Laboratory)

Abstract

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.

Suggested Citation

  • W. Geremew & N. M. Nam & A. Semenov & V. Boginski & E. Pasiliao, 2018. "A DC programming approach for solving multicast network design problems via the Nesterov smoothing technique," Journal of Global Optimization, Springer, vol. 72(4), pages 705-729, December.
    • Handle: RePEc:spr:jglopt:v:72:y:2018:i:4:d:10.1007_s10898-018-0671-9
    DOI: 10.1007/s10898-018-0671-9
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    References listed on IDEAS

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    1. Nguyen Mau Nam & R. Blake Rector & Daniel Giles, 2017. "Minimizing Differences of Convex Functions with Applications to Facility Location and Clustering," Journal of Optimization Theory and Applications, Springer, vol. 173(1), pages 255-278, April.
    2. Gerhard Reinelt, 1991. "TSPLIB—A Traveling Salesman Problem Library," INFORMS Journal on Computing, INFORMS, vol. 3(4), pages 376-384, November.
    3. NESTEROV, Yu., 2005. "Smooth minimization of non-smooth functions," LIDAM Reprints CORE 1819, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    2. Kai Tu & Haibin Zhang & Huan Gao & Junkai Feng, 2020. "A hybrid Bregman alternating direction method of multipliers for the linearly constrained difference-of-convex problems," Journal of Global Optimization, Springer, vol. 76(4), pages 665-693, April.

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