Author

Alex L. Wang

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Preprint Sep 2026

A Unified Theory of H-Duality in First-Order Methods

We provide two complementary explanations of H-duality in smooth strongly convex optimization and contractive fixed-point problems. H-duality refers to the phenomenon where the worst-case performance of many fixed-step first-order methods (FSFOMs) for a given performance setup are exactly equal to the worst-case perfor...

Kevin Shu, Alex L. Wang · 2 citations

Preprint Jul 2026

Implicit Primal-Dual Guarantees in Unconstrained First-Order Minimization

It is shown that any first-order method guaranteeing a bound on the primal objective gap f(x_N)-f(x_\star) assuming only a bound on $\|x_0-x_\star\|$ actually has a stronger guarantee on an explicit, computable primal-dual gap at the same rate.

Benjamin Grimmer, Alex L. Wang · 0 citations