proximal-newton method

Variants of the A-HPE and large-step A-HPE algorithms for strongly convex problems with applications to accelerated high-order tensor methods

  • M. Marques Alves
    • Categories Convex and Nonsmooth Optimization Tags , , , , , , ,

    For solving strongly convex optimization problems, we propose and study the global convergence of variants of the A-HPE and large-step A-HPE algorithms of Monteiro and Svaiter. We prove \emph{linear} and the \emph{superlinear} $\mathcal{O}\left(k^{\,-k\left(\frac{p-1}{p+1}\right)}\right)$ global rates for the proposed variants of the A-HPE and large-step A-HPE methods, respectively. The parameter $p\geq 2$ appears in the (high-order) … Read more

    A proximal-Newton method for unconstrained convex optimization in Hilbert spaces

  • M. Marques Alves
  • Benar Fux Svaiter
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    We propose and study the iteration-complexity of a proximal-Newton method for finding approximate solutions of the problem of minimizing a twice continuously differentiable convex function on a (possibly infinite dimensional) Hilbert space. We prove global convergence rates for obtaining approximate solutions in terms of function/gradient values. Our main results follow from an iteration-complexity study of … Read more

    An inexact proximal path-following algorithm for constrained convex minimization

  • Volkan Cevher
  • Quoc Tran-Dinh
  • Anastasios Kyrillidis
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    Many scientific and engineering applications feature large-scale non-smooth convex minimization problems over convex sets. In this paper, we address an important instance of this broad class where we assume that the non-smooth objective is equipped with a tractable proximity operator and that the convex constraints afford a self-concordant barrier. We provide a new joint treatment … Read more