An interior-point method for the single-facility location problem with mixed norms using a conic formulation

Robert Chares and François Glineur

No 2007071, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: We consider the single-facility location problem with mixed norms, i.e. the problem of minimizing the sum of the distances from a point to a set of fixed points in R, where each distance can be measured according to a different p-norm.We show how this problem can be expressed into a structured conic format by decomposing the nonlinear components of the objective into a series of constraints involving three-dimensional cones. Using the availability of a self-concordant barrier for these cones, we present a polynomial-time algorithm (a long-step path-following interior-point scheme) to solve the problem up to a given accuracy. Finally, we report computational results for this algorithm and compare with standard nonlinear optimization solvers applied to this problem.

Keywords: nonsymmetric conic optimization; conic reformulation; convex optimization; sum of norm minimization; single-facility location problems; interior-point methods (search for similar items in EconPapers)
Date: 2007-09-01
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Related works:
Working Paper: An interior-point method for the single-facility location problem with mixed norms using a conic formulation (2009)
Journal Article: An interior-point method for the single-facility location problem with mixed norms using a conic formulation (2008)
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