Formulae of Epigraphical Projection for Solving Minimax Location Problems

We are interested in a numerical method for solving extended multifacility minimax location problems introduced by Drezner in 1991. For this purpose, we present some formulae of projections onto the epigraphs of the sum of powers of weighted norms and onto the epigraphs of gauges. By bringing the extended multifacility location problem into a form of an unconstrained optimization problem where its objective function is a sum of functions allows us then to use the parallel splitting algorithm in combination with the introduced projection formulae to solve this kind of location problems. Numerical experiments document the usefulness of our approach for the discussed location problems.