Geovani Nunes Grapiglia

On the Complexity of an Augmented Lagrangian Method for Nonconvex Optimization

  • Geovani Nunes Grapiglia
  • Ya-xiang Yuan
    • Categories Nonlinear Optimization Tags , , ,

    In this paper we study the worst-case complexity of an inexact Augmented Lagrangian method for nonconvex constrained problems. Assuming that the penalty parameters are bounded, we prove a complexity bound of $\mathcal{O}(|\log(\epsilon)|)$ outer iterations for the referred algorithm to generate an $\epsilon$-approximate KKT point, for $\epsilon\in (0,1)$. When the penalty parameters are unbounded, we prove … Read more

    Tensor Methods for Minimizing Convex Functions with Hölder Continuous Higher-Order Derivatives

  • Geovani Nunes Grapiglia
  • Yurii Nesterov
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , ,

    In this paper we study p-order methods for unconstrained minimization of convex functions that are p-times differentiable with $\nu$-Hölder continuous pth derivatives. We propose tensor schemes with and without acceleration. For the schemes without acceleration, we establish iteration complexity bounds of $\mathcal{O}\left(\epsilon^{-1/(p+\nu-1)}\right)$ for reducing the functional residual below a given $\epsilon\in (0,1)$. Assuming that $\nu$ … Read more