nonconvex

Alternating projections on manifolds

  • Adrian Lewis
  • Jérôme Malick
    • Categories Constrained Nonlinear Optimization Tags , , , , , ,

    We prove that if two smooth manifolds intersect transversally, then the method of alternating projections converges locally at a linear rate. We bound the speed of convergence in terms of the angle between the manifolds, which in turn we relate to the modulus of metric regularity for the intersection problem, a natural measure of conditioning. … Read more

    A Robust Gradient Sampling Algorithm for Nonsmooth, Nonconvex Optimization

  • James V. Burke
  • Adrian Lewis
  • Michael L. Overton
    • Categories Nonsmooth Optimization Tags , ,

    Let $f$ be a continuous function on $\Rl^n$, and suppose $f$ is continuously differentiable on an open dense subset. Such functions arise in many applications, and very often minimizers are points at which $f$ is not differentiable. Of particular interest is the case where $f$ is not convex, and perhaps not even locally Lipschitz, but … Read more