Variational Analysis and Optimization Seminar

In this talk, we first discuss a connection between the Halpern fixed-point iteration and Nesterov's accelerated schemes for a root-finding problem involving a co-coercive operator. We also study this connection for different recent schemes, including extra anchored gradient method and its variants. We show how the convergence results from one scheme can be transferred to another. Next, we develop a randomized block-coordinate algorithm for solving the above root-finding problem, which is different from existing randomized coordinate methods in optimization. Finally, we consider the applications of this randomized coordinate scheme to monotone inclusions and finite-sum monotone inclusions. The latter one can be applied to a federated learning setting. Speaker(s): Quoc Tran-Dinh (University of North Carolina at Chapel Hill)