Abstract
The Euclidean single facility location problem (ESFL) and the Euclidean multiplicity location problem (EMFL) are two special nonsmooth convex programming problems which have attracted a large literature. For the ESFL problem, there are algorithms which converge both globally and quadratically. For the EMFL problem, there are some quadratically convergent algorithms, but for global convergence, they all need nontrivial assumptions on the problem.
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