Francesco Rinaldi

A weak tail-bound probabilistic condition for function estimation in stochastic derivative-free optimization

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

    In this paper, we use tail bounds to define a tailored probabilistic condition for function estimation that eases the theoretical analysis of stochastic derivative-free optimization methods. In particular, we focus on the unconstrained minimization of a potentially non-smooth function, whose values can only be estimated via stochastic observations, and give a simplified convergence proof for … 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

    An oracle-based framework for robust combinatorial optimization

  • Enrico Bettiol
  • Christoph Buchheim
  • Marianna De Santis
  • Francesco Rinaldi
    • Categories Global Optimization, Robust Optimization Tags , ,

    We propose a general solution approach for min-max-robust counterparts of combinatorial optimization problems with uncertain linear objectives. We focus on the discrete scenario case, but our approach can be extended to other types of uncertainty sets such as polytopes or ellipsoids. Concerning the underlying certain problem,the algorithm is entirely oracle-based, i.e., our approach only requires … Read more

    An Improved Penalty Algorithm using Model Order Reduction for MIPDECO problems with partial observations

  • Dominik Garmatter
  • Margherita Porcelli
  • Francesco Rinaldi
  • Martin Stoll
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs Tags , , , ,

    This work addresses optimal control problems governed by a linear time-dependent partial differential equation (PDE) as well as integer constraints on the control. Moreover, partial observations are assumed in the objective function. The resulting problem poses several numerical challenges due to the mixture of combinatorial aspects, induced by integer variables, and large scale linear algebra … Read more

    Minimization over the l1-ball using an active-set non-monotone projected gradient

  • Andrea Cristofari
  • Marianna De Santis
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , ,

    The l1-ball is a nicely structured feasible set that is widely used in many fields (e.g., machine learning, statistics and signal analysis) to enforce some sparsity in the model solutions. In this paper, we devise an active-set strategy for efficiently dealing with minimization problems over the l1-ball and embed it into a tailored algorithmic scheme … 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

    A Unifying Framework for Sparsity Constrained Optimization

  • Matteo Lapucci
  • Tommaso Levato
  • Francesco Rinaldi
  • Marco Sciandrone
    • Categories Constrained Nonlinear Optimization, Global Optimization Theory, Statistics Tags , , , , ,

    In this paper, we consider the optimization problem of minimizing a continuously differentiable function subject to both convex constraints and sparsity constraints. By exploiting a mixed-integer reformulation from the literature, we define a necessary optimality condition based on a tailored neighborhood that allows to take into account potential changes of the support set. We then … 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

    A derivative-free method for structured optimization problems

  • Andrea Cristofari
  • Francesco Rinaldi
    • Categories Nonlinear Optimization

    Structured optimization problems are ubiquitous in fields like data science and engineering. The goal in structured optimization is using a prescribed set of points, called atoms, to build up a solution that minimizes or maximizes a given function. In the present paper, we want to minimize a black-box function over the convex hull of a … Read more