Compare parameter restrictions with prior multioperator Douglas–Rachford methods

Determine whether the parameter conditions for the multioperator Douglas–Rachford methods of AT25 and ADT25 are more restrictive than the parameter conditions obtained for the generalized splitting framework presented in the paper.

Background

The paper compares its generalized splitting framework with the multioperator Douglas–Rachford algorithms studied in AT25 and ADT25. Although the paper identifies several differences in assumptions—such as permutation-invariant conditions on semimonotonicity moduli—it does not establish a complete comparison of the admissible parameter ranges. The relative restrictiveness of the parameter conditions therefore remains unresolved.

References

As in the previous subsection, the convergence conclusions obtained in the present work recover those in ; the main difference lies in the assumptions and in the admissible parameter ranges, although it is not immediately clear to us whether the parameter conditions in are more restrictive than those required in the present work.

— A Splitting Framework for Composite Semimonotone Inclusions  (2608.16609 - Alcantara et al., 17 Aug 2026) in Section 5.3, subsection “Multioperator Douglas–Rachford algorithm under generalized monotonicity and comonotonicity”