A note on optimality conditions for the Euclidean. Multifacility location problem |
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Authors: | Achiya Dax |
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Institution: | (1) Hydrologicla Service, P.O. Box 6381, 91060 Jerusalem, Israel |
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Abstract: | Thekey problem of the Euclidean multifacility location (EMFL) problem is to decide whether a givendead point is optimal. If it is not optimal, we wish to compute a descent direction. This paper extends the optimality conditions of
Calamai and Conn and Overton to the case when the rows of the active constraints matrix are linearly dependent. We show that
linear dependence occurs wheneverG, the graph of the coinciding facilities, has a cycle. In this case the key problem is formulated as a linear least squares
problem with bounds on the Euclidean norms of certain subvectors. |
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Keywords: | Multifacility location problem optimality conditions graph theory incidence matrix cycles bounded linear least squares |
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