This paper is concerned with efficient algorithms for solving Weber problem, which is an important problem arising in the facility location problems. In this paper, we reformulate the Weber problem as its equivalent form and then propose a semismooth Newton based augmented Lagrangian (SSNAL) algorithm for solving Weber problem. The global convergence and locally asymptotically superlinear convergence of the SSNAL algorithm are characterized under mild conditions. Numerical experiments conducted on synthetic data sets demonstrate that the SSNAL algorithm outperforms several state-of-the-art algorithms in terms of efficiency and robustness.
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