An interior point algorithm for solving continuous single- or multifacility
location problems is presented. Distances can be measured with arbitrary,
possibly nonsymmetric gauges, while the globalizing function which combines
these distances into a global objective function value is assumed to be a
convex quadratic and monotonically nondecreasing function.
Using the notion of self-concordant barrier functions,
it is shown that the algorithm computes an $\varepsilon$-approximation to a
minimum of the objective function with a number of floating point operations
which is bounded by a polynomial in the input size and~$\log(1/\varepsilon)$.
The algorithm can be extended to the case in which the globalizing
function contains additionally the maximum of some of the distances.
The complexity result holds for this case also.
Keywords. multifacility location, continuous location,
interior point algorithms, barrier methods, polynomiality, gauges, convexity.