Francesco Rinaldi

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

    Mining for diamonds – matrix generation algorithms for binary quadratically constrained quadratic problems

  • Enrico Bettiol
  • Immanuel M. Bomze
  • Lucas Létocart
  • Francesco Rinaldi
  • Emiliano Traversi
    • Categories (Mixed) Integer Nonlinear Programming, Linear, Cone and Semidefinite Programming Tags , , ,

    In this paper, we consider binary quadratically constrained quadratic problems and propose a new approach to generate stronger bounds than the ones obtained using the Semidefinite Programming relaxation. The new relaxation is based on the Boolean Quadric Polytope and is solved via a Dantzig-Wolfe Reformulation in matrix space. For block-decomposable problems, we extend the relaxation … Read more

    Solving non-monotone equilibrium problems via a DIRECT-type approach

  • Stefano Lucidi
  • Mauro Passacantando
  • Francesco Rinaldi
    • Categories Complementarity and Variational Inequalities, Global Optimization Tags , , ,

    A global optimization approach for solving non-monotone equilibrium problems (EPs) is proposed. The class of (regularized) gap functions is used to reformulate any EP as a constrained global optimization program and some bounds on the Lipschitz constant of such functions are provided. The proposed global optimization approach is a combination of an improved version of … Read more

    Zero Order Stochastic Weakly Convex Composite Optimization

  • Vyacheslav Kungurtsev
  • Francesco Rinaldi
    • Categories Nonlinear Optimization, Nonsmooth Optimization, Stochastic Programming Tags , , ,

    In this paper we consider stochastic weakly convex composite problems, however without the existence of a stochastic subgradient oracle. We present a derivative free algorithm that uses a two point approximation for computing a gradient estimate of the smoothed function. We prove convergence at a similar rate as state of the art methods, however with … Read more