Two Adaptive Accelerated Golden Ratio Primal--Dual Algorithms With an Application to Poisson Imaging Problem

What the math gives to ML

The paper provides a practical primal-dual splitting scheme for composite objectives whose differentiable term is only locally smooth, avoiding a known global gradient-Lipschitz constant, a manual step-size cap, and a linesearch. The transferable asset is the combination of golden-ratio extrapolation with online curvature adaptation: the optimizer can react to local gradient variation while retaining bounded step sizes and ergodic convergence for convex subproblems. A useful neural-network adaptation is a constrained or composite optimizer for parameter blocks, where weight regularization is handled by a primal proximal step, auxiliary constraints by a dual proximal step, and the data loss supplies the locally smooth gradient. The strongest initial test should use convex last-layer training or LoRA with fixed features, where the paper's assumptions are meaningful, before testing the same update as a nonconvex heuristic on full networks.