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A continuation approach for the capacitated multi-facility weber problem based on nonlinear SOCP reformulation

Jein-Shan Chen Shaohua Pan Chun-Hsu Ko

Optimization and Control mathscidoc:1910.43915

Journal of Global Optimization, 50, (4), 713-728, 2011.8
We propose a primal-dual continuation approach for the capacitated multi-facility Weber problem (CMFWP) based on its nonlinear second-order cone program (SOCP) reformulation. The main idea of the approach is to reformulate the CMFWP as a nonlinear SOCP with a nonconvex objective function, and then introduce a logarithmic barrier term and a quadratic proximal term into the objective to construct a sequence of convexified subproblems. By this, this class of nondifferentiable and nonconvex optimization problems is converted into the solution of a sequence of nonlinear convex SOCPs. In this paper, we employ the semismooth Newton method proposed in Kanzow etal. (SIAM Journal of Optimization 20:297320, 2009) to solve the KKT system of the resulting convex SOCPs. Preliminary numerical results are reported for eighteen test instances, which indicate that the continuation approach is
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@inproceedings{jein-shan2011a,
  title={A continuation approach for the capacitated multi-facility weber problem based on nonlinear SOCP reformulation},
  author={Jein-Shan Chen, Shaohua Pan, and Chun-Hsu Ko},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224653024424444},
  booktitle={Journal of Global Optimization},
  volume={50},
  number={4},
  pages={713-728},
  year={2011},
}
Jein-Shan Chen, Shaohua Pan, and Chun-Hsu Ko. A continuation approach for the capacitated multi-facility weber problem based on nonlinear SOCP reformulation. 2011. Vol. 50. In Journal of Global Optimization. pp.713-728. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020224653024424444.
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