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math.OC2026
Log-Averaged Mirror Prox for Fast, Large-Scale Optimal Transport in Linear Space
Matthew X. Burns, Jiaming Liang
We propose Log-Averaged Mirror Prox (LAMP), a linear-space primal-dual method for large-scale optimal transport. LAMP implements primal mirror prox updates by tracking an averaged…
math.OC2026
Accuracy Certificates for Convex Optimization at Accelerated Rates via Primal-Dual Averaging
Matthew X. Burns, Jiaming Liang
Many works in convex optimization provide rates for achieving a small primal gap. However, this quantity is typically unavailable in practice. In this work, we show that solving a…
math.OC2026
Improved Analysis of Restarted Accelerated Gradient and Augmented Lagrangian Methods via Inexact Proximal Point Frameworks
Matthew X. Burns, Jiaming Liang
This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradi…