P-norm minimization over intersections of convex sets

We consider the minimization of the ℓ_p norm subject to convex constraints. The problem considered in this paper may be regarded as a relaxation of a similar problem that employs the ℓ₁ norm. We derive the dual problem, which is unconstrained and devise an algorithm for the dual problem by adapting the Douglas-Rachford algorithm. We demonstrate the utility of the algorithm on an experiment and discuss its differences with an existing algorithm.