Matthew X. Burns

Log-Averaged Mirror Prox for Fast, Large-Scale Optimal Transport in Linear Space

  • Matthew X. Burns
  • Jiaming Liang
    • Categories Convex Optimization, Parallel Algorithms Tags , , , ,

    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 dual sequence, reducing storage complexity from \({O}(nm)\) to \({O}(n+m)\) while preserving dense, GPU-friendly reductions. Consequently, LAMP preserves the last-iterate \(\widetilde{{O}}( nm\varepsilon^{-1})\) arithmetic complexity of conservatively parameterized primal-dual mirror prox. We further … Read more

    Accuracy Certificates for Convex Optimization at Accelerated Rates via Primal-Dual Averaging

  • Matthew X. Burns
  • Jiaming Liang
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , ,

    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 regularized surrogate with algorithms based on simple primal-dual averaging provides non-asymptotic convergence guarantees for a computable optimality certificate. We first analyze primal and dual methods based … Read more

    Improved Analysis of Restarted Accelerated Gradient and Augmented Lagrangian Methods via Inexact Proximal Point Frameworks

  • Matthew X. Burns
  • Jiaming Liang
    • Categories Constrained Nonlinear Optimization, Convex and Nonsmooth Optimization, Convex Optimization Tags , , , ,

    This paper studies a class of double-loop (inner-outer) algorithms for convex composite optimization. For unconstrained problems, we develop a restarted accelerated composite gradient method that attains the optimal first-order complexity in both the convex and strongly convex settings. For linearly constrained problems, we introduce inexact augmented Lagrangian methods, including a basic method and an outer-accelerated … Read more