worst-case

A Riemannian AdaGrad-Norm Method

  • Glaydston Bento
  • Geovani Nunes Grapiglia
  • Mauricio Louzeiro
  • Daoping Zhang
    • Categories Generalized Convexity/Monoticity, Global Optimization Applications, Nonlinear Optimization Tags , , , ,

    We propose a manifold AdaGrad-Norm method (\textsc{MAdaGrad}), which extends the norm version of AdaGrad (AdaGrad-Norm) to Riemannian optimization. In contrast to line-search schemes, which may require several exponential map computations per iteration, \textsc{MAdaGrad} requires only one. Assuming the objective function $f$ has Lipschitz continuous Riemannian gradient, we show that the method requires at most $\mathcal{O}(\varepsilon^{-2})$ … Read more

    How much patience do you have? A worst-case perspective on smooth nonconvex optimization

  • Coralia Cartis
  • Nicholas I. M. Gould
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , ,

    The paper presents a survey of recent results in the field of worst-case complexity of algorithms for nonlinear (and possibly nonconvex) smooth optimization. Both constrained and unconstrained case are considered. ArticleDownload View PDF