ON MINIMAL EXTENDED REPRESENTATIONS OF GENERALIZED POWER CONES.

In this paper, we analyze minimal representations of (p, α)-power cones as simpler cones. We derive some new results on the complexity of the representations, and we provide a procedure to construct a minimal representation by means of second order cones in case α and p are rational. The construction is based on the identification of the cones with a graph, the mediated graph. Then, we develop a mixed integer linear optimization formulation to obtain the optimal mediated graph, and then the minimal representation. We present the results of a series of computational experiments in order to analyze the computational performance of the approach, both to obtain the representation and its incorporation into a practical conic optimization model that arises in facility location. [ABSTRACT FROM AUTHOR]