Multivariate Monotone Inclusions in Saddle Form

Understand

We propose a novel approach to monotone operator splitting based on the notion of a saddle operator.

• Under investigation is 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.
• A limitation of existing primal-dual algorithms is that they operate in a product space that is too small to achieve full splitting of our problem in the sense that each operator is used individually.