Winner
Benjamin Grimmer (Johns Hopkins Department of Applied Math and Statistics)
Citation
Benjamin Grimmer is awarded the 2025 INFORMS Optimization Society Young Researchers Prize for his paper “Provably Faster Gradient Descent via Long Steps”, SIAM Journal on Optimization 34.3 (2024): 2588-2608.
For decades, it was unknown whether stepsizes longer than those guaranteeing per-iteration descent could improve the convergence of gradient descent for smooth convex optimization. The cited paper resolves this long-standing open question with a breakthrough result: carefully designed cyclic schedules that periodically include long steps provably achieve strictly better worst-case guarantees than the classical constant-stepsize method, even though individual iterates may temporarily worsen the objective. Methodologically, the work departs sharply from traditional one-step induction analyses by leveraging a computer-assisted performance-estimation framework. It introduces a “straightforwardness” property for stepsize schedules that can be certified via a semidefinite program, enabling automated discovery and proof of effective long-step patterns. In contrast to its more common role of confirming or refining existing analyses, here, performance estimation enabled the derivation of an unexpected result. The paper has already drawn broad interest and inspired substantial follow-up research, establishing a new foundation for our understanding of gradient descent.
Prize committee
Merve Bodur (chair), Frank Curtis, Paul Grigas, Guanghai Lan, Joseph Paat