SOLVING GEOMETRIC AND L_P-NORM OPTIMIZATION PROBLEMS WITH A CONIC FORMULATION

Geometric and l_p-norm optimization form two classes of well-studied convex problems
that exhibit better duality properties than the general case (namely a zero duality
gap).

These problems have been formulated recently as conic programs with the aid of
suitably defined convex cones (these cones were not self-dual, contrary to the
well-studied cases of linear, second-order and semidefinite optimization problems).
This lead to easier proofs of their duality properties, making use of the machinery
of standard conic duality.

In this talk, we present self-concordant barriers for these cones, allowing thus the
design of polynomial interior-point algorithms to solve these two classes of
problems. We also investigate the use of a self-dual embedding to avoid the need to
know an initial strictly feasible point.