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1 Foundations of Computing and Decision Sciences

1 2000

1 Glineur F.

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An extended conic formulation for geometric optimization

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Glineur F.

tom Vol. 25, No. 3

161-174

The author has recently proposed a new way of formulating two classical classes of structured convex problems, geometric and lp-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 lp-norm optimization, which opens the way to a common generalization.