Geodesic
Lagrangian relaxations for the nonlinear $p$-median problem
The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 2, pp. 45-59

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In this paper we study a modification of well-known $p$-median problem, in which the number of facilities is a non-fixed value. We consider the problem statement and propose a heuristic method to get lower bounds of the optimal values.
Keywords: the $p$-median problem, Lagrangian relaxation, lower bounds; subgradient algorithm. 
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     author = {I. L. Vasiliev and A. V. Ushakov},
     title = {Lagrangian relaxations for the nonlinear $p$-median problem},
     journal = {The Bulletin of Irkutsk State University. Series Mathematics},
     pages = {45--59},
     publisher = {mathdoc},
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     url = {http://geodesic.mathdoc.fr/item/IIGUM_2011_4_2_a3/}
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I. L. Vasiliev; A. V. Ushakov. Lagrangian relaxations for the nonlinear $p$-median problem. The Bulletin of Irkutsk State University. Series Mathematics, Tome 4 (2011) no. 2, pp. 45-59. http://geodesic.mathdoc.fr/item/IIGUM_2011_4_2_a3/