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

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Abstract

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 et al. (SIAM Journal of Optimization 20:297–320, 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 promising to find a satisfying suboptimal solution, even a global optimal solution for some test problems.

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Authors and Affiliations

  1. Department of Mathematics, National Taiwan Normal University, 11677, Taipei, Taiwan

    Jein-Shan Chen

  2. School of Mathematical Sciences, South China University of Technology, 510640, Guangzhou, China

    Shaohua Pan

  3. Department of Electrical Engineering, I-Shou University, 840, Kaohsiung, Taiwan

    Chun-Hsu Ko

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  1. Jein-Shan Chen
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  2. Shaohua Pan
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  3. Chun-Hsu Ko
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Correspondence to Jein-Shan Chen.

Additional information

J.-S. Chen—Member of Mathematics Division, National Center for Theoretical Sciences, Taipei Office.

The author’s work is partially supported by National Science Council of Taiwan.

S. Pan—The author’s work is supported by the Fundamental Research Funds for the Central Universities (SCUT), Guangdong Natural Science Foundation (No. 9251802902000001) and National Young Natural Science Foundation (No. 10901058).

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Chen, JS., Pan, S. & Ko, CH. A continuation approach for the capacitated multi-facility weber problem based on nonlinear SOCP reformulation. J Glob Optim 50, 713–728 (2011). https://doi.org/10.1007/s10898-010-9632-7

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