Accelerated Algorithms for Monotone Inclusions

This lecture by Quoc Tran-Dinh presents Halpern-type accelerated and splitting algorithms for monotone inclusions, focusing on optimization models and applications in various fields like convex optimization, nonlinear analysis, economics, and machine learning. The talk covers the motivation behind monotone inclusions, the optimization model, the challenges in developing accelerated methods, and the derivation of new algorithms like Halpern fixed-point iteration and splitting extra-gradient methods. The lecture also discusses the properties of maximally monotone operators, Lipschitz continuity, resolvent and proximal operators, convergence rates, and complexity analysis tools. The presentation concludes with the comparison of different methods and the convergence analysis of the proposed accelerated algorithms.