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 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.