Abstract: We investigate a highly structured multivariate monotone inclusion problem involving a mix of set-valued, cocoercive, and Lipschitzian monotone operators, as well as various monotonicity-preserving operations among them. This model encompasses most formulations found in the literature. However, devising a solution method for it does not seem possible with existing tools. Thus, we propose a novel approach to monotone operator splitting based on the notion of a saddle operator. This leads to an algorithm of unprecedented flexibility, which achieves full splitting, uses the specific attributes of each operator, is asynchronous, and requires to activate only blocks of operators at each iteration, as opposed to all of them. Applications are presented. Joint work with Patrick L. Combettes.
Multivariate Monotone Inclusions in Saddle Form
02.05.2023 09:45 - 10:45
Organiser:
R. I. Bot, E. R. Csetnek, Y. Malitskyi, H. Schichl
Location: