derivative-free methods

Complexity results and active-set identification of a derivative-free method for bound-constrained problems

  • Andrea Brilli
  • Andrea Cristofari
  • Giampaolo Liuzzi
  • Stefano Lucidi
    • Categories Bound-constrained Optimization, Nonlinear Optimization Tags , ,

    In this paper, we analyze a derivative-free line search method designed for bound-constrained problems. Our analysis demonstrates that this method exhibits a worst-case complexity comparable to other derivative-free methods for unconstrained and linearly constrained problems. In particular, when minimizing a function with $n$ variables, we prove that at most ${\cal O}(n\epsilon^{-2})$ iterations are needed to … Read more

    Quadratic Regularization Methods with Finite-Difference Gradient Approximations

  • Geovani Nunes Grapiglia
    • Categories Nonlinear Optimization Tags , , ,

    This paper presents two quadratic regularization methods with finite-difference gradient approximations for smooth unconstrained optimization problems. One method is based on forward finite-difference gradients, while the other is based on central finite-difference gradients. In both methods, the accuracy of the gradient approximations and the regularization parameter in the quadratic models are jointly adjusted using a … Read more

    Accelerated derivative-free nonlinear least-squares applied to the estimation of Manning coefficients

  • Ernesto G. Birgin
  • José Mario Martínez
    • Categories Nonlinear Systems and Least-Squares Tags , , ,

    A general framework for solving nonlinear least squares problems without the employment of derivatives is proposed in the present paper together with a new general global convergence theory. With the aim to cope with the case in which the number of variables is big (for the standards of derivative-free optimization), two dimension-reduction procedures are introduced. … 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

    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