lipschitz functions

Dini Derivative and a Characterization for Lipschitz and Convex Functions on Riemannian Manifolds

  • Orizon Pereira Ferreira
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Nonsmooth Optimization Tags , , ,

    Dini derivative on Riemannian manifold setting is studied in this paper. In addition, a characterization for Lipschitz and convex functions defined on Riemannian manifolds and sufficient optimality conditions for constraint optimization problems in terms of the Dini derivative are given. ArticleDownload View PDF

    Convergence Analysis of the DIRECT Algorithm

  • D. E. Finkel
  • C. T. Kelley
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Nonsmooth Optimization Tags , , ,

    The DIRECT algorithm is a deterministic sampling method for bound constrained Lipschitz continuous optimization. We prove a subsequential convergence result for the DIRECT algorithm that quantifies some of the convergence observations in the literature. Our results apply to several variations on the original method, including one that will handle general constraints. We use techniques from … Read more