Deriving online OGM via a non-augmented estimate sequence

Determine whether a non-augmented estimate sequence framework can be used to derive the original online Optimized Gradient Method (OGM) without resorting to augmentation.

Background

The paper introduces primal-dual estimate functions (PDEF) that generalize classical estimate sequences and allow the construction of an Optimized Gradient Method with Memory (OGMM) possessing state-of-the-art worst-case guarantees. To connect with existing analyses of the Optimized Gradient Method (OGM), the authors show that augmenting their estimate sequence leads to potential functions used in prior work.

Despite this connection through augmentation, it remains unresolved whether an estimate sequence—without augmentation—can directly yield the original online OGM. Clarifying this would unify methodologies and potentially offer a more transparent derivation of OGM within the estimate-sequence framework.