Constrained convex minimization via model-based excessive gap

Abstract

We introduce a model-based excessive gap technique to analyze first-order primal-dual methods for constrained convex minimization. As a result, we construct new primal-dual methods with optimal convergence rates on the objective residual and the primal feasibility gap of their iterates separately. Through a dual smoothing and prox-function selection strategy, our framework subsumes the augmented La-grangian, and alternating methods as special cases, where our rates apply. 1