We study a conical extension of averaged nonexpansive operators and the role it plays in convergence analysis fixed point algorithms. Various properties conically are systematically investigated, particular, stability under relaxations, convex combinations compositions. derive averagedness resolvents generalized monotone operators. These then utilized order to analyze proximal algorithm, forwar...

We develop stochastic first-order primal-dual algorithms to solve a class of convex-concave saddle-point problems. When the saddle function is strongly convex in primal variable, we first restart scheme for this problem. gradient noises obey sub-Gaussian distributions, oracle complexity our strictly better than any existing methods, even deterministic case. Furthermore, each problem parameter i...