Acceleration and Extrapolation Methods

Solving systems of nonlinear equations and optimization problems are pervasive issues throughout the mathematical sciences with applications in many areas. Acceleration and extrapolation methods have emerged as a key technology to solve these problems efficiently and robustly. The simple underlying idea of these methods is to recombine previous approximations in a sequence to determine the next term or approximation. This approach has been applied repeatedly and from different angles to numerous problems over the last several decades. Important methods including epsilon algorithms and Anderson acceleration were introduced throughout the early and mid-20th century, and are now common in many applied fields including optimization, machine learning, computational chemistry, materials, and climate sciences. Within the last decade, theoretical advances on convergence, acceleration mechanisms, and the development of unified frameworks to understand these methods have come to light, yet our understanding remains incomplete. Fascinating links exist with methods such as Nesterov acceleration and other momentum-based approaches that have been developed in the fields of optimization and machine learning in the past decades. These links and connections with dynamical systems appear to be promising directions for further insight that remain largely unexplored. The goals of this workshop include assessing the state of the art and exploring connections between closely related methods that may have been independently developed; connecting theory to practice by fostering interaction between theorists and applied practitioners; and, encouraging new and continuing collaborations between participants.