Francesco Rinaldi

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

    Nonmonotone GRASP

  • Marianna De Santis
  • Paola Festa
  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Meta Heuristics Tags , , , , ,

    A Greedy Randomized Adaptive Search Procedure (GRASP) is an iterative multistart metaheuristic for difficult combinatorial optimization problems. Each GRASP iteration consists of two phases: a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Repeated applications … Read more

    Derivative-free Robust Optimization for Circuit Design

  • A. Ciccazzo
  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Francesco Rinaldi
  • V. Latorre
    • Categories Nonlinear Optimization, Robust Optimization Tags

    In this paper, we introduce a framework for derivative-free robust optimization based on the use of an efficient derivative-free optimization routine for mixed integer nonlinear problems. The proposed framework is employed to find a robust optimal design of a particular integrated circuit (namely a DC-DC converter commonly used in portable electronic devices). The proposed robust … Read more

    A Derivative-Free Algorithm for Constrained Global Optimization based on Exact Penalty Functions

  • G. Di Pillo
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Global Optimization, Nonlinear Optimization

    Constrained global optimization problems can be tackled by using exact penalty approaches. In a preceding paper, we proposed an exact penalty algorithm for constrained problems which combines an unconstrained global minimization technique for minimizing a non-differentiable exact penalty func- tion for given values of the penalty parameter, and an automatic updating of the penalty parameter … Read more

    A variable fixing version of the two-block nonlinear constrained Gauss-Seidel algorithm for ℓ1-regularized least-squares

  • Margherita Porcelli
  • Francesco Rinaldi
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , ,

    The problem of finding sparse solutions to underdetermined systems of linear equations is very common in many fields as e.g. in signal/image processing and statistics. A standard tool for dealing with sparse recovery is the ℓ1-regularized least-squares approach that has recently attracted the attention of many researchers. In this paper, we describe a new version … Read more

    A Linesearch-based Derivative-free Approach for Nonsmooth Optimization

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

    In this paper, we propose new linesearch-based methods for nonsmooth optimization problems when first-order information on the problem functions is not available. In the first part, we describe a general framework for bound-constrained problems and analyze its convergence towards stationary points, using the Clarke-Jahn directional derivative. In the second part, we consider inequality constrained optimization … Read more

    A class of derivative-free nonmonotone optimization algorithms employing coordinate rotations and gradient approximations

  • Luigi Grippo
  • Francesco Rinaldi
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , ,

    In this paper we study a class of derivative-free unconstrained minimization algorithms employing nonmonotone inexact linesearch techniques along a set of suitable search directions. In particular, we define globally convergent nonmonotone versions of some well-known derivative-free methods and we propose a new algorithm combining coordinate rotations with approximate simplex gradients. Through extensive numerical experimentation, we … Read more

    Derivative-free methods for constrained mixed-integer optimization

  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories (Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization Tags , ,

    We consider the problem of minimizing a continuously di erentiable function of several variables subject to simple bound and general nonlinear inequality constraints, where some of the variables are restricted to take integer values. We assume that the rst order derivatives of the objective and constraint functions can be neither calculated nor approximated explicitly. This class … Read more

    An Exact Penalty Global Optimization Approach for Mixed-Integer Programming Problems

  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    In this work, we propose a global optimization approach for mixed-integer programming problems. To this aim, we preliminarily de ne an exact penalty algorithm model for globally solving general problems and we show its convergence properties. Then, we describe a particular version of the algorithm that solves mixed integer problems. Citation DIS Technical Report n. 17, … Read more

    DERIVATIVE-FREE METHODS FOR BOUND CONSTRAINED MIXED-INTEGER OPTIMIZATION

  • Giampaolo Liuzzi
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories (Mixed) Integer Nonlinear Programming, Bound-constrained Optimization Tags , ,

    We consider the problem of minimizing a continuously differentiable function of several variables subject to simple bound constraints where some of the variables are restricted to take integer values. We assume that the first order derivatives of the objective function can be neither calculated nor approximated explicitly. This class of mixed integer nonlinear optimization problems … Read more