Robustly stable accelerated momentum methods with a near-optimal L₂ gain and H∞ performance

Mathematics of Operations Research, 2025. Dedicated to Michael L. Overton.

Publisher (DOI)

Treats first-order algorithms as feedback dynamical systems subject to worst-case, finite-energy gradient errors and computes their H∞ norm in closed form on quadratics — together with the explicit worst-case noise achieving it (a decaying cosine). Introduces robustly stable variants (RS-GD, RS-HB) with near-optimal L₂ gain, quantifies real stability radii of momentum methods, and extends the guarantees beyond quadratics through matrix-inequality certificates.

Momentum & accelerationRisk & robustnessSpectral & nonsmooth optimization

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• Entropic risk-averse generalized momentum methods (Optim. Methods Softw., 2025)
• Robust accelerated primal-dual methods for computing saddle points (SIAM J. Optim., 2024)
• Differentially private accelerated optimization algorithms (SIAM J. Optim., 2022)