AN EXTENDED CONIC FORMULATION FOR GEOMETRIC OPTIMIZATION

The author has recently proposed a new way of formulating two classical
classes of structured convex problems, geometric and l_p-norm optimization,
using dedicated convex cones. This approach has some advantages over the
traditional formulation: it simplifies the proofs of the well-known associated
duality properties (i.e. weak and strong duality) and the design of a
polynomial algorithm becomes straightforward.

In this article, we make a step towards the description of a common framework
that includes these two classes of problems. Indeed, we present an extended
variant of the cone for geometric optimization previously introduced by the
author and show it is equally suitable to formulate this class of problems.
This new cone has the additional advantage of being very similar to the cone
used for l_p-norm optimization, which opens the way to a common generalization.