Francesco Rinaldi

An algorithmic framework based on primitive directions and nonmonotone line searches for black box problems with integer variables

  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Integer Programming, Optimization Software and Modeling Systems

    In this paper, we develop a new algorithmic framework that handles black box problems with integer variables. The strategy included in the framework makes use of specific search directions (so called primitive directions) and a suitably developed nonmonotone line search, thus guaranteeing a high level of freedom when exploring the integer lattice. We first describe … Read more

    A General Regularized Continuous Formulation for the Maximum Clique Problem

  • James T. Hungerford
  • Francesco Rinaldi
    • Categories Combinatorial Optimization, Network Optimization, Nonlinear Optimization Tags , , , ,

    In this paper, we develop a general regularization-based continuous optimization framework for the maximum clique problem. In particular, we consider a broad class of regularization terms that can be included in the classic Motzkin-Strauss formulation and we develop conditions that guarantee the equivalence between the continuous regularized problem and the original one in both a … Read more

    A simplicial decomposition framework for large scale convex quadratic programming

  • Enrico Bettiol
  • Lucas Létocart
  • Francesco Rinaldi
  • Emiliano Traversi
    • Categories Convex Optimization, Quadratic Programming Tags , , ,

    In this paper, we analyze in depth a simplicial decomposition like algorithmic framework for large scale convex quadratic programming. In particular, we first propose two tailored strategies for handling the master problem. Then, we describe a few techniques for speeding up the solution of the pricing problem. We report extensive numerical experiments on both real … Read more

    An Active-Set Algorithmic Framework for Non-Convex Optimization Problems over the Simplex

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

    In this paper, we describe a new active-set algorithmic framework for minimizing a non-convex function over the unit simplex. At each iteration, the method makes use of a rule for identifying active variables (i.e., variables that are zero at a stationary point) and specific directions (that we name active-set gradient related directions) satisfying a new … Read more

    A Two-Stage Active-Set Algorithm for Bound-Constrained Optimization

  • Andrea Cristofari
  • Marianna De Santis
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Bound-constrained Optimization

    In this paper, we describe a two-stage method for solving optimization problems with bound constraints. It combines the active-set estimate described in [Facchinei and Lucidi, 1995] with a modification of the non-monotone line search framework recently proposed in [De Santis et al., 2012]. In the first stage, the algorithm exploits a property of the active-set … Read more

    A DERIVATIVE-FREE APPROACH TO CONSTRAINED MULTIOBJECTIVE NONSMOOTH OPTIMIZATION

  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    In this work, we consider multiobjective optimization problems with both bound constraints on the variables and general nonlinear constraints, where objective and constraint function values can only be obtained by querying a black box. We define a linesearch-based solution method, and we show that it converges to a set of Pareto stationary points. To this … Read more

    A Frank-Wolfe Based Branch-and-Bound Algorithm for Mean-Risk Optimization

  • Christoph Buchheim
  • Marianna De Santis
  • Francesco Rinaldi
  • Long Trieu
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    We present an exact algorithm for mean-risk optimization subject to a budget constraint, where decision variables may be continuous or integer. The risk is measured by the covariance matrix and weighted by an arbitrary monotone function, which allows to model risk-aversion in a very individual way. We address this class of convex mixed-integer minimization problems … Read more

    A Feasible Active Set Method with Reoptimization for Convex Quadratic Mixed-Integer Programming

  • Christoph Buchheim
  • Marianna De Santis
  • Stefano Lucidi
  • Francesco Rinaldi
  • Long Trieu
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , ,

    We propose a feasible active set method for convex quadratic programming problems with non-negativity constraints. This method is specifically designed to be embedded into a branch-and-bound algorithm for convex quadratic mixed integer programming problems. The branch-and-bound algorithm generalizes the approach for unconstrained convex quadratic integer programming proposed by Buchheim, Caprara and Lodi to the presence … Read more

    A Fast Active Set Block Coordinate Descent Algorithm for l1-regularized least squares

  • Marianna De Santis
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Convex and Nonsmooth Optimization, Nonlinear Systems and Least-Squares Tags , ,

    The problem of finding sparse solutions to underdetermined systems of linear equations arises in several real-world problems (e.g. signal and image processing, compressive sensing, statistical inference). A standard tool for dealing with sparse recovery is the l1-regularized least-squares approach that has been recently attracting the attention of many researchers. In this paper, we describe an … Read more

    Derivative-free Methods for Mixed-Integer Constrained Optimization Problems

  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Constrained Nonlinear Optimization

    Methods which do not use any derivative information are becoming popular among researchers, since they allow to solve many real-world engineering problems. Such problems are frequently characterized by the presence of discrete variables which can further complicate the optimization process. In this paper, we propose derivative-free algorithms for solving continuously differentiable Mixed Integer NonLinear Programming … Read more