M. Dodangeh

On the optimal order of worst case complexity of direct search

  • M. Dodangeh
  • Luis Nunes Vicente
  • Z. Zhang
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , , ,

    The worst case complexity of direct-search methods has been recently analyzed when they use positive spanning sets and impose a sufficient decrease condition to accept new iterates. Assuming that the objective function is smooth, it is now known that such methods require at most O(n^2 epsilon^{-2}) function evaluations to compute a gradient of norm below … Read more

    Worst case complexity of direct search under convexity

  • M. Dodangeh
  • Luis Nunes Vicente
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , ,

    In this paper we prove that the broad class of direct-search methods of directional type, based on imposing sufficient decrease to accept new iterates, exhibits the same global rate or worst case complexity bound of the gradient method for the unconstrained minimization of a convex and smooth function. More precisely, it will be shown that … Read more