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math.OC2026
Improved Gradient Complexity for Quasi-Newton Proximal Extragradient Methods via Certified Curvature Reuse
Aryan Mokhtari, Francisco Patitucci
We study how curvature estimated from gradient differences can accelerate proximal-extragradient quasi-Newton methods. Existing global guarantees for QNPE, A-QNPE, and OL-OQN learn…
math.OC2025
Improving Online-to-Nonconvex Conversion for Smooth Optimization via Double Optimism
Francisco Patitucci, Ruichen Jiang, Aryan Mokhtari
A recent breakthrough in nonconvex optimization is the online-to-nonconvex conversion framework of [Cutkosky et al., 2023], which reformulates the task of finding an -…
math.OC2024
Improved Complexity for Smooth Nonconvex Optimization: A Two-Level Online Learning Approach with Quasi-Newton Methods
Ruichen Jiang, Aryan Mokhtari, Francisco Patitucci
We study the problem of finding an -first-order stationary point (FOSP) of a smooth function, given access only to gradient information. The best-known gradient query complexity…