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 O(1 / ε) efficiency estimate. The performance of the algorithm is demonstrated by solving large instances of the convex sparse recovery problem.
- Complexity/rate of convergence analysis
- First order methods
- Nonsmooth convex minimization
- Sparse recovery
- l-norm minimization