APPROXIMATING GEOMETRIC OPTIMIZATION WITH $L_P$-NORM OPTIMIZATION

In this article, we demonstrate how to approximate geometric optimization with
l_p-norm optimization. These two categories of problems are well known in
structured convex optimization. We describe a family of l_p-norm optimization
problems that can be made arbitrarily close to a geometric optimization
problem, and show that the dual problems for these approximations are also
approximating the dual geometric optimization problem. Finally, we use these
approximations and the duality theory for l_p-norm optimization to derive
simple proofs of the weak and strong duality theorems for geometric
optimization.