accelerated composite gradient method

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

    An Average Curvature Accelerated Composite Gradient Method for Nonconvex Smooth Composite Optimization Problems

  • Jiaming Liang
  • Renato D.C. Monteiro
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , ,

    This paper presents an accelerated composite gradient (ACG) variant, referred to as the AC-ACG method, for solving nonconvex smooth composite minimization problems. As opposed to well-known ACG variants that are either based on a known Lipschitz gradient constant or a sequence of maximum observed curvatures, the current one is based on a sequence of average … Read more