Damiano Zeffiro

Stochastic trust-region and direct-search methods: A weak tail bound condition and reduced sample sizing

  • Francesco Rinaldi
  • Luis Nunes Vicente
  • Damiano Zeffiro
    • Categories Nonsmooth Optimization, Stochastic Programming, Unconstrained Optimization Tags , , ,

    Using tail bounds, we introduce a new probabilistic condition for function estimation in stochastic derivative-free optimization which leads to a reduction in the number of samples and eases algorithmic analyses. Moreover, we develop simple stochastic direct-search and trust-region methods for the optimization of a potentially non-smooth function whose values can only be estimated via stochastic … Read more

    Retraction based Direct Search Methods for Derivative Free Riemannian Optimization

  • Vyacheslav Kungurtsev
  • Francesco Rinaldi
  • Damiano Zeffiro
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    Direct search methods represent a robust and reliable class of algorithms for solving black-box optimization problems. In this paper, we explore the application of those strategies to Riemannian optimization, wherein minimization is to be performed with respect to variables restricted to lie on a manifold. More specifically, we consider classic and line search extrapolated variants … Read more

    Frank-Wolfe and friends: a journey into projection-free first-order optimization methods

  • Immanuel M. Bomze
  • Francesco Rinaldi
  • Damiano Zeffiro
    • Categories Convex Optimization, Nonlinear Optimization Tags , , , ,

    Invented some 65 years ago in a seminal paper by Marguerite Straus-Frank and Philip Wolfe, the Frank-Wolfe method recently enjoys a remarkable revival, fuelled by the need of fast and reliable first-order optimization methods in Data Science and other relevant application areas. This review tries to explain the success of this approach by illustrating versatility … Read more

    Fast cluster detection in networks by first-order optimization

  • Immanuel M. Bomze
  • Francesco Rinaldi
  • Damiano Zeffiro
    • Categories Network Optimization, Nonlinear Optimization Tags , , ,

    Cluster detection plays a fundamental role in the analysis of data. In this paper, we focus on the use of s-defective clique models for network-based cluster detection and propose a nonlinear optimization approach that efficiently handles those models in practice. In particular, we introduce an equivalent continuous formulation for the problem under analysis, and we … Read more

    A unifying framework for the analysis of projection-free first-order methods under a sufficient slope condition

  • Francesco Rinaldi
  • Damiano Zeffiro
    • Categories Nonlinear Optimization Tags , , , ,

    The analysis of projection-free first order methods is often complicated by the presence of different kinds of “good” and “bad” steps. In this article, we propose a unifying framework for projection-free methods, aiming to simplify the converge analysis by getting rid of such a distinction between steps. The main tool employed in our framework is … Read more

    Active Set Complexity of the Away-step Frank-Wolfe Algorithm

  • Immanuel M. Bomze
  • Francesco Rinaldi
  • Damiano Zeffiro
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , ,

    In this paper, we study active set identification results for the away-step Frank-Wolfe algorithm in different settings. We first prove a local identification property that we apply, in combination with a convergence hypothesis, to get an active set identification result. We then prove, in the nonconvex case, a novel O(1/ √k) convergence rate result and … Read more