smooth optimization

Searching for Optimal Per-Coordinate Step-sizes with Multidimensional Backtracking

  • Frederik Kunstner
  • Mark Schmidt
    • Categories Convex Optimization, Nonlinear Optimization Tags , ,

    The backtracking line-search is an effective technique to automatically tune the step-size in smooth optimization. It guarantees similar performance to using the theoretically optimal step-size. Many approaches have been developed to instead tune per-coordinate step-sizes, also known as diagonal preconditioners, but none of the existing methods are provably competitive with the optimal per-coordinate stepsizes. We … Read more

    A Local MM Subspace Method for Solving Constrained Variational Problems in Image Recovery

  • Émilie Chouzenoux
  • Ségolène Martin
  • Jean-Christophe Pesquet
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , , , ,

    This article introduces a new Penalized Majorization-Minimization Subspace algorithm (P-MMS) for solving smooth, constrained optimization problems. In short, our approach consists of embedding a subspace algorithm in an inexact exterior penalty procedure. The subspace strategy, combined with a Majoration-Minimization step-size search, takes great advantage of the smoothness of the penalized cost function, while the penalty … Read more

    Limited-memory Common-directions Method for Large-scale Optimization: Convergence, Parallelization, and Distributed Optimization

  • Ching-pei Lee
  • Po-Wei Wang
  • Chih-Jen Lin
    • Categories Parallel Algorithms, Unconstrained Optimization Tags , , ,

    In this paper, we present a limited-memory common-directions method for smooth optimization that interpolates between first- and second- order methods. At each iteration, a subspace of a limited dimension size is constructed using first-order information from previous iterations, and an ef- ficient Newton method is deployed to find an approximate minimizer within this subspace. With … Read more

    OSGA: A fast subgradient algorithm with optimal complexity

  • Arnold Neumaier
    • Categories Convex Optimization, Nonsmooth Optimization Tags , , , , , , , ,

    This paper presents an algorithm for approximately minimizing a convex function in simple, not necessarily bounded convex domains, assuming only that function values and subgradients are available. No global information about the objective function is needed apart from a strong convexity parameter (which can be put to zero if only convexity is known). The worst … Read more