convex conjugate

A unified framework for Bregman proximal methods: subgradient, gradient, and accelerated gradient schemes

  • David H. Gutman
  • Javier F. Peña
    • Categories Convex Optimization Tags , , , ,

    We provide a unified framework for analyzing the convergence of Bregman proximal first-order algorithms for convex minimization. Our framework hinges on properties of the convex conjugate and gives novel proofs of the convergence rates of the Bregman proximal subgradient, Bregman proximal gradient, and a new accelerated Bregman proximal gradient algorithm under fairly general and mild … Read more

    Convergence rates of proximal gradient methods via the convex conjugate

  • David H. Gutman
  • Javier F. Peña
    • Categories Convex Optimization Tags , ,

    We give a novel proof of the $O(1/k)$ and $O(1/k^2)$ convergence rates of the proximal gradient and accelerated proximal gradient methods for composite convex minimization. The crux of the new proof is an upper bound constructed via the convex conjugate of the objective function. Citation Technical Report, Carnegie Mellon University, January 2018. Article Download View … Read more

    Convergence of first-order methods via the convex conjugate

  • Javier F. Peña
    • Categories Convex Optimization Tags ,

    This paper gives a unified and succinct approach to the $O(1/\sqrt{k}), O(1/k),$ and $O(1/k^2)$ convergence rates of the subgradient, gradient, and accelerated gradient methods for unconstrained convex minimization. In the three cases the proof of convergence follows from a generic bound defined by the convex conjugate of the objective function. Citation Working Paper, Carnegie Mellon … Read more