期刊名称：CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度：2007
卷号：1
出版社：Center for Operations Research and Econometrics (UCL), Louvain
摘要：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 Rn, 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 threedimensional
cones.
Using the availability of a self-concordant barrier for these cones, we present a polynomialtime
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.
关键词：nonsymmetric conic optimization, conic reformulation, convex optimization,
sum of norm minimization, single-facility location problems, interior-point methods.
