An extended conic formulation for geometric optimization

The author has recently proposed a new way of formulating two classical\nclasses of structured convex problems, geometric and l_p-norm optimization,\nusing dedicated convex cones. This approach has some advantages over the\ntraditional formulation: it simplifies the proofs of the well-known associated\nduality properties (i.e. weak and strong duality) and the design of a\npolynomial algorithm becomes straightforward.\nIn this article, we make a step towards the description of a common framework\nthat includes these two classes of problems. Indeed, we present an extended\nvariant of the cone for geometric optimization previously introduced by the\nauthor and show it is equally suitable to formulate this class of problems.\nThis new cone has the additional advantage of being very similar to the cone\nused for l_p-norm optimization, which opens the way to a common generalization.