Two unconstrained optimization approaches for the Euclidean -centrum location problem

Shaohua Pan Jein-Shan Chen

Numerical Analysis and Scientific Computing mathscidoc:1910.43934

Applied mathematics and computation, 189, (2), 1368-1383
Consider the single-facility Euclidean -centrum location problem in R n. This problem is a generalization of the classical Euclidean 1-median problem and 1-center problem. In this paper, we develop two efficient algorithms that are particularly suitable for problems where n is large by using unconstrained optimization techniques. The first algorithm is based on the neural networks smooth approximation for the plus function and reduces the problem to an unconstrained smooth convex minimization problem. The second algorithm is based on the FischerBurmeister merit function for the second-order cone complementarity problem and transforms the KKT system of the second-order cone programming reformulation for the problem into an unconstrained smooth minimization problem. Our computational experiments indicate that both methods are extremely efficient for large problems and the first algorithm is able to
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@inproceedings{shaohuatwo,
  title={Two unconstrained optimization approaches for the Euclidean -centrum location problem},
  author={Shaohua Pan, and Jein-Shan Chen},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225238493707463},
  booktitle={Applied mathematics and computation},
  volume={189},
  number={2},
  pages={1368-1383},
}
Shaohua Pan, and Jein-Shan Chen. Two unconstrained optimization approaches for the Euclidean -centrum location problem. Vol. 189. In Applied mathematics and computation. pp.1368-1383. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020225238493707463.
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