Kellie J. MacPhee

Stochastic model-based minimization under high-order growth

  • Damek Davis
  • Dmitriy Drusvyatskiy
  • Kellie J. MacPhee
    • Categories Convex and Nonsmooth Optimization Tags , , , ,

    Given a nonsmooth, nonconvex minimization problem, we consider algorithms that iteratively sample and minimize stochastic convex models of the objective function. Assuming that the one-sided approximation quality and the variation of the models is controlled by a Bregman divergence, we show that the scheme drives a natural stationarity measure to zero at the rate $O(k^{-1/4})$. … Read more

    Foundations of gauge and perspective duality

  • Aleksandr Y. Aravkin
  • James V. Burke
  • Dmitriy Drusvyatskiy
  • Michael P. Friedlander
  • Kellie J. MacPhee
    • Categories Convex Optimization Tags , , ,

    Common numerical methods for constrained convex optimization are predicated on efficiently computing nearest points to the feasible region. The presence of a design matrix in the constraints yields feasible regions with more complex geometries. When the functional components are gauges, there is an equivalent optimization problem—the gauge dual– where the matrix appears only in the … Read more