Faster Lagrangian-Based Methods in Convex Optimization

In this paper, we aim at unifying, simplifying, and improving the convergence rate analysis of Lagrangian-based methods for convex optimization problems. We first introduce notion nice primal algorithmic map, which plays a central role in unification simplification most methods. Equipped with then versatile generic scheme, allows design faster Lagrangian (FLAG) new provably sublinear expressed terms function values feasibility violation original (nonergodic) generated sequence. To demonstrate power versatility our approach results, show that well-known iconic schemes admit map hence share results within their corresponding FLAG.