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. These new proofs rely on the
general duality theory valid for convex problems expressed in conic form and
the work on polynomial interior-point methods by Nesterov and Nemirovsky.

In this paper, we make a step towards the description of a common framework
that would include these two classes of problems. Indeed, we introduce 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.