Abstract
A unified and numerically stable second-order approach to the continuous multifacility location problem is presented. Although details are initially given for only the unconstrained Euclidean norm problem, we show how the framework can be readily extended to l p norm and mixed norm problem as well as to constrained problems.
Since the objective function being considered is not everywhere differentiable the straightforward application of classical solution procedures is infeasible. The method presented is an extension of an earlier first-order technique of the authors and is based on certain non-orthogonal projections. For efficiency the linear substructures that are inherent in the problem are exploited in the implementation of the basic algorithm and in the manner of handling degeneracies and near-properties of the problem. Moreover, the advantages that we derive from the linear substructures are equally applicable to small-scale and large-scale problems.
Some preliminary numerical results and comparisons are included.
This work was supported in part by Natural Science and Engineering Research Council of Canada Grant No. A8639.
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Calamai, P.H., Conn, A.R. (1982). A second-order method for solving the continuous multifacility location problem. In: Watson, G.A. (eds) Numerical Analysis. Lecture Notes in Mathematics, vol 912. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0093145
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DOI: https://doi.org/10.1007/BFb0093145
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