Worst-Case Complexity Bounds

An Adaptive Riemannian Gradient Method Without Function Evaluations

  • Geovani Nunes Grapiglia
  • Gabriel Stella
    • Categories Nonlinear Optimization Tags , ,

    In this paper we propose an adaptive gradient method for optimization on Riemannian manifolds. The update rule for the stepsizes relies only on gradient evaluations. Assuming that the objective function is bounded from below and that its gradient field is Lipschitz continuous, we establish worst-case complexity bounds for the number of gradient evaluations that the … Read more

    Adaptive Third-Order Methods for Composite Convex Optimization

  • Geovani Nunes Grapiglia
  • Yurii Nesterov
    • Categories Convex Optimization Tags , ,

    In this paper we propose third-order methods for composite convex optimization problems in which the smooth part is a three-times continuously differentiable function with Lipschitz continuous third-order derivatives. The methods are adaptive in the sense that they do not require the knowledge of the Lipschitz constant. Trial points are computed by the inexact minimization of … Read more