restart

A Parameter-Free Restart Scheme with Only a Parallelizable $\log\log(1/\epsilon)$ Overhead

  • Yue Wu
  • Benjamin Grimmer
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , ,

    It is well-known that first-order methods can offer accelerated convergence rates in the presence of growth structures. Restarting schemes provide a general tool for such speed-ups. These schemes typically either require unrealistic problem knowledge, incur logarithmic overhead factors in oracle complexity, and/or have a nontrivial initial burn-in phase. We present a parameter-free approach for restarting … Read more

    The superiorization method with restarted perturbations for split minimization problems with an application to radiotherapy treatment planning

  • Francisco J. Aragón Artacho
  • Yair Censor
  • Aviv Gibali
  • David Torregrosa-Belén
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Convex Optimization Tags , , , , , ,

    In this paper we study the split minimization problem that consists of two constrained minimization problems in two separate spaces that are connected via a linear operator that maps one space into the other. To handle the data of such a problem we develop a superiorization approach that can reach a feasible point with reduced … Read more

    A Simple Nearly-Optimal Restart Scheme For Speeding-Up First-Order Methods

  • Benjamin Grimmer
  • James Renegar
    • Categories Convex Optimization, Nonsmooth Optimization Tags , ,

    We present a simple scheme for restarting first-order methods for convex optimization problems. Restarts are made based only on achieving specified decreases in objective values, the specified amounts being the same for all optimization problems. Unlike existing restart schemes, the scheme makes no attempt to learn parameter values characterizing the structure of an optimization problem, … Read more

    CONVERGENCE RATE OF GRADIENT BASED ADAPTIVE RESTART FOR ACCELERATED GRADIENT SCHEMES

  • Shivkumar Chandrasekaran
  • Ming Gu
  • Can Kizilkale
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    The accelerated gradient algorithm is known to have non-monotonic, periodic convergence behavior in the high momentum regime. If important function parameters like the condition number are known, the momentum can be adjusted to get linear convergence. Unfortunately these parameters are usually not accessible, so instead heuristics are used for deciding when to restart. One of … Read more