A Dc Programming Approach For Solving Multicast Network Design Problems Via The Nesterov Smoothing Technique
Keywords
DC programming; Fenchel conjugate; Hierarchical clustering; Nesterov’s smoothing techniques; Subgradient
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.
Publication Date
12-1-2018
Publication Title
Journal of Global Optimization
Volume
72
Issue
4
Number of Pages
705-729
Document Type
Article
Personal Identifier
scopus
DOI Link
https://doi.org/10.1007/s10898-018-0671-9
Copyright Status
Unknown
Socpus ID
85048364267 (Scopus)
Source API URL
https://api.elsevier.com/content/abstract/scopus_id/85048364267
STARS Citation
Geremew, W.; Nam, N. M.; Semenov, A.; Boginski, V.; and Pasiliao, E., "A Dc Programming Approach For Solving Multicast Network Design Problems Via The Nesterov Smoothing Technique" (2018). Scopus Export 2015-2019. 10264.
https://stars.library.ucf.edu/scopus2015/10264