Deterministic Adam-Inspired Methods with Accelerated Convergence Rate
Adam is widely used, but its convergence theory remains incomplete even in the deterministic full-batch setting because momentum and adaptive preconditioning are tightly coupled. For smooth convex objectives, we split the momentum variable through variable-and-operator splitting, which reveals the acceleration mechanism. We then combine a Hessian-driven correction with Adam-style feedback based on the gradient magnitude. The resulting Adam-HNAG (Hessian-driven Nesterov accelerated gradient with Adam-style adaptive preconditioning) flow admits a nonnegative energy that decays exponentially. Its discretization yields two methods, Adam-HNAG and the synchronous variant Adam-HNAG-s. Under the ...
| Authors | Yaxin Yu, Long Chen, Zeyi Xu |
|---|---|
| Primary category | math.OC |
| Published | 9 April 2026 |
| Last updated at source | 16 August 2026 |
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