Author

Benjamin Grimmer

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Preprint Sep 2026

On Minimax Optimality and Uniqueness of Fixed-Step First-Order Methods for Smooth Convex Optimization

This paper considers the design of optimal fixed-step first-order methods for high-dimensional minimization of $L$-smooth convex functions. For optimizing worst-case performance measured via suboptimality of the final function value (relative to the initial squared distance to a minimizer), we provide an algebraic proo...

Benjamin Grimmer, Sunghyeon Jo, Chanwoo Park · 1 citation

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