An interior-point method for the single-facility location problem with mixed norms using a conic formulation
(2008) Mathematical Methods of Operations Research — Vol. 68, n° 3, p. 383-405 (2008)
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- 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.
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Citations
Chares, R., & Glineur, F. (2008). An interior-point method for the single-facility location problem with mixed norms using a conic formulation. Mathematical Methods of Operations Research, 68(3), 383-405. https://doi.org/10.1007/s00186-008-0225-x (Original work published 2008)