A dual method for minimizing a nonsmooth objective over one smooth inequality constraint

We consider the class of nondifferentiable convex problems which minimizes a nonsmooth convex objective over a single smooth constraint. Exploiting the smoothness of the feasible set and using duality, we introduce a simple first order algorithm proven to globally converge to an optimal solution with a efficiency estimate. The performance of the algorithm is demonstrated by solving large instances of the convex sparse recovery problem.