Stefano Lucidi

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 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

    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

    New concave penalty functions for improving the Feasibility Pump

  • Marianna De Santis
  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories (Mixed) Integer Linear Programming, Nonlinear Optimization Tags , , ,

    Mixed-Integer optimization represents a powerful tool for modeling many optimization problems arising from real-world applications. The Feasibility pump is a heuristic for finding feasible solutions to mixed integer linear problems. In this work, we propose a new feasibility pump approach using concave non-differentiable penalty functions for measuring solution integrality. We present computational results on binary … Read more

    Exact Penalty Functions for Nonlinear Integer Programming Problems

  • Stefano Lucidi
  • Francesco Rinaldi
    • Categories Integer Programming, Nonlinear Optimization Tags , ,

    In this work, we study exact continuous reformulations of nonlinear integer programming problems. To this aim, we preliminarily state conditions to guarantee the equivalence between pairs of general nonlinear problems. Then, we prove that optimal solutions of a nonlinear integer programming problem can be obtained by using various exact penalty formulations of the original problem … Read more

    A nonmonotone truncated Newton-Krylov method exploiting negative curvature directions, for large scale unconstrained optimization: complete results

  • Giovanni Fasano
  • Stefano Lucidi
    • Categories Unconstrained Optimization Tags , , , ,

    We propose a new truncated Newton method for large scale unconstrained optimization, where a Conjugate Gradient (CG)-based technique is adopted to solve Newton’s equation. In the current iteration, the Krylov method computes a pair of search directions: the first approximates the Newton step of the quadratic convex model, while the second is a suitable negative … Read more

    An algorithm model for mixed variable programming

  • Stefano Lucidi
  • Veronica Piccialli
  • Marco Sciandrone
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    In this paper we consider a particular class of nonlinear optimization problems involving both continuous and discrete variables. The distinguishing feature of this class of nonlinear mixed optimization problems is that the structure and the number of variables of the problem depend on the values of some discrete variables. In particular we define a general … Read more

    New Classes of Globally Convexized Filled Functions for Global Optimization

  • Stefano Lucidi
  • Veronica Piccialli
    • Categories Global Optimization Theory, Nonlinear Optimization Tags , ,

    We propose new classes of globally convexized filled functions. Unlike the globally convexized filled functions previously proposed in literature, the ones proposed in this paper are continuously differentiable and, under suitable assumptions, their unconstrained minimization allows to escape from any local minima of the original objective function. Moreover we show that the properties of the … Read more