Lijun Ding

Sharpness and well-conditioning of nonsmooth convex formulations in statistical signal recovery

  • Lijun Ding
  • Alex L. Wang
    • Categories Nonsmooth Optimization, Optimization in Data Science, Statistics Tags , , , , ,

    We study a sample complexity vs. conditioning tradeoff in modern signal recovery problems where convex optimization problems are built from sampled observations. We begin by introducing a set of condition numbers related to sharpness in \(\ell_p\) or Schatten-p norms (\(p\in[1,2]\)) based on nonsmooth reformulations of a class of convex optimization problems, including sparse recovery, low-rank … Read more

    Low-rank matrix recovery with composite optimization: good conditioning and rapid convergence

  • Vasileios Charisopoulos
  • Damek Davis
  • Mateo Díaz
  • Dmitriy Drusvyatskiy
  • Yudong Chen
  • Lijun Ding
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    The task of recovering a low-rank matrix from its noisy linear measurements plays a central role in computational science. Smooth formulations of the problem often exhibit an undesirable phenomenon: the condition number, classically defined, scales poorly with the dimension of the ambient space. In contrast, we here show that in a variety of concrete circumstances, … Read more