Robust algorithms for online convex problems via primal-dual

The importance of primal-dual methods in online optimization can hardly be overstated, and they give several of the state-of-the art results in both of the most common models for online algorithms: the adversarial and the stochastic/random order models. Here we try to provide a more unified analysis of primal-dual algorithms to better understand the mechanisms behind this important method. With this we are able of recover and extend in one goal several results of the literature.