Technical Note—Solving Constrained Multi-Facility Location Problems Involving l_p Distances Using Convex Programming

A method is described for approximating nondifferentiable convex minimization problems occurring in location theory by differentiable problems. Distances are generalized to l_p distances that include rectangular and Euclidean distances as special cases. Any number of linear and/or nonlinear constraints can be accommodated. The method utilizes a hyperbolic distance function that is uniformly convergent to each l_p distance. Computational results are reported.