Technical Note - Solving Constrained Multi-Facility Location Problems Involving lp 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 lp 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 lp distance. Computational results are reported.