Sequential smoothing framework for convex-concave saddle point problems with application to large-scale constrained optimization

In this paper, we propose a sequential smoothing algorithm for solving large scale convex-concave saddle point problems. We prove that this class of algorithms achieves the convergence rate O(1/√ε) in the deterministic setting and O(1/√ε) with probability at least 1 - δ, where δ ϵ (0, 1), in the stochastic setting, to obtain an g-optimal solution. We then apply our general algorithm to specific problems in large-scale convex constrained optimization.