Smooth minimization of non-smooth functions

In this paper we introduce a new primal-dual technique for convergence analysis of gradient schemes for nonsmooth convex optimization. As an example of its application, we derive a primal-dual gradient method for a special class of structured nonsmooth ...

In this paper we suggest new dual methods for solving variational inequalities with monotone operators. We show that with an appropriate step-size strategy, our method is optimal both for Lipschitz continuous operators ( $$O({1 \over \epsilon})$$ ...

In this paper we extend the smoothing technique (Nesterov in Math Program 103(1): 127---152, 2005; Nesterov in Unconstrained convex mimimization in relative scale, 2003) onto the problems of semidefinite optimization. For that, we develop a simple ...