A projection method forl _{ p } norm locationallocation problems
 Ingrid Bongartz,
 Paul H. Calamai,
 Andrew R. Conn
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We present a solution method for locationallocation problems involving thel _{ p } norm, where 1 <p < ∞. The method relaxes the {0, 1} constraints on the allocations, and solves for both the locations and allocations simultaneously. Necessary and sufficient conditions for local minima of the relaxed problem are stated and used to develop an iterative algorithm. This algorithm finds a stationary point on a series of subspaces defined by the current set of activities. The descent direction is a projection onto the current subspace of a direction incorporating secondorder information for the locations, and firstorder information for the allocations. Under mild conditions, the algorithm finds local minima with {0, 1} allocations and exhibits quadratic convergence. An implementation that exploits the special structure of these problems to dramatically reduce the computational cost of the required numerical linear algebra is described. Numerical results for thirtysix test problems are included.
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 Title
 A projection method forl _{ p } norm locationallocation problems
 Journal

Mathematical Programming
Volume 66, Issue 13 , pp 283312
 Cover Date
 19940801
 DOI
 10.1007/BF01581151
 Print ISSN
 00255610
 Online ISSN
 14364646
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Locationallocation problem
 Generalized Weber problem
 Projection methods
 Active set methods
 Relaxation methods
 Nonsmooth optimization
 Industry Sectors
 Authors

 Ingrid Bongartz ^{(1)}
 Paul H. Calamai ^{(2)}
 Andrew R. Conn ^{(1)}
 Author Affiliations

 1. Thomas J. Watson Research Center, IBM Corporation, P.O. Box 218, 10598, Yorktown Heights, NY, USA
 2. Department of Systems Design Engineering, University of Waterloo, N2L 3G1, Waterloo, Ontario, Canada