Convex ordered median problem with ℓpℓp-norms

This paper presents a procedure to solve the convex ordered median problem where the distances are measured with ℓpℓp-norms. In order to do that, we consider an approximated problem and develop an algorithm based on a gradient descent method that generates a sequence with decreasing objective value. We prove its convergence to the optimal solution of the approximated problem. The paper ends with some computational results of the proposed methodology.