derivative-free optimization

Improving the Flexibility and Robustness of Model-Based Derivative-Free Optimization Solvers

  • Coralia Cartis
  • Jan Fiala
  • Benjamin Marteau
  • Lindon Roberts
    • Categories Nonlinear Optimization Tags , , , , ,

    We present DFO-LS, a software package for derivative-free optimization (DFO) for nonlinear Least-Squares (LS) problems, with optional bound constraints. Inspired by the Gauss-Newton method, DFO-LS constructs simplified linear regression models for the residuals. DFO-LS allows flexible initialization for expensive problems, whereby it can begin making progress from as few as two objective evaluations. Numerical results … Read more

    Derivative-Free Optimization of Noisy Functions via Quasi-Newton Methods

  • Albert S. Berahas
  • Richard H. Byrd
  • Jorge Nocedal
    • Categories Nonlinear Optimization, Unconstrained Optimization Tags , ,

    This paper presents a finite difference quasi-Newton method for the minimization of noisy functions. The method takes advantage of the scalability and power of BFGS updating, and employs an adaptive procedure for choosing the differencing interval h based on the noise estimation techniques of Hamming (2012) and Moré and Wild (2011). This noise estimation procedure … Read more

    The Mesh Adaptive Direct Search Algorithm for Granular and Discrete Variables

  • Charles Audet
  • Sébastien Le Digabel
  • Christophe Tribes
    • Categories Nonlinear Optimization Tags , , , ,

    The mesh adaptive direct search (Mads) algorithm is designed for blackbox optimization problems for which the functions defining the objective and the constraints are typically the outputs of a simulation seen as a blackbox. It is a derivative-free optimization method designed for continuous variables and is supported by a convergence analysis based on the Clarke … Read more

    A note on using performance and data profiles for training algorithms

  • Margherita Porcelli
  • Philippe L. Toint
    • Categories Nonlinear Optimization, Optimization of Simulated Systems, Optimization Software Benchmark Tags , , ,

    It is shown how to use the performance and data profile benchmarking tools to improve algorithms’ performance. An illustration for the BFO derivative-free optimizer suggests that the obtained gains are potentially significant. CitationACM Transactions on Mathematical Software, 45:2 (2019), Article 20.ArticleDownload View PDF

    A derivative-free Gauss-Newton method

  • Coralia Cartis
  • Lindon Roberts
    • Categories Nonlinear Optimization Tags , , , , ,

    We present DFO-GN, a derivative-free version of the Gauss-Newton method for solving nonlinear least-squares problems. As is common in derivative-free optimization, DFO-GN uses interpolation of function values to build a model of the objective, which is then used within a trust-region framework to give a globally-convergent algorithm requiring $O(\epsilon^{-2})$ iterations to reach approximate first-order criticality … Read more

    Derivative-Free Robust Optimization by Outer Approximations

  • Matt Menickelly
  • Stefan M. Wild
    • Categories Nonsmooth Optimization, Robust Optimization, Unconstrained Optimization Tags , , ,

    We develop an algorithm for minimax problems that arise in robust optimization in the absence of objective function derivatives. The algorithm utilizes an extension of methods for inexact outer approximation in sampling a potentially infinite-cardinality uncertainty set. Clarke stationarity of the algorithm output is established alongside desirable features of the model-based trust-region subproblems encountered. We … Read more

    Manifold Sampling for Optimization of Nonconvex Functions that are Piecewise Linear Compositions of Smooth Components

  • Kamil Khan
  • Jeffrey Larson
  • Stefan M. Wild
    • Categories Nonsmooth Optimization, Unconstrained Optimization Tags , ,

    We develop a manifold sampling algorithm for the minimization of a nonsmooth composite function $f \defined \psi + h \circ F$ when $\psi$ is smooth with known derivatives, $h$ is a known, nonsmooth, piecewise linear function, and $F$ is smooth but expensive to evaluate. The trust-region algorithm classifies points in the domain of $h$ as … Read more

    Direct Search Methods on Reductive Homogeneous Spaces

  • Dreisigmeyer David
    • Categories Nonlinear Optimization, Nonsmooth Optimization Tags ,

    Direct search methods are mainly designed for use in problems with no equality constraints. However, there are many instances where the feasible set is of measure zero in the ambient space and no mesh point lies within it. There are methods for working with feasible sets that are (Riemannian) manifolds, but not all manifolds are … Read more

    Direct search based on probabilistic feasible descent for bound and linearly constrained problems

  • Serge Gratton
  • Clément W. Royer
  • Luis Nunes Vicente
  • Z. Zhang
    • Categories Bound-constrained Optimization, Nonlinear Optimization, Stochastic Programming Tags , , , , ,

    Direct search is a methodology for derivative-free optimization whose iterations are characterized by evaluating the objective function using a set of polling directions. In deterministic direct search applied to smooth objectives, these directions must somehow conform to the geometry of the feasible region and typically consist of positive generators of approximate tangent cones (which then … Read more

    Locally weighted regression models for surrogate-assisted design optimization

  • Charles Audet
  • Michael Kokkolaras
  • Sébastien Le Digabel
  • Bastien Talgorn
    • Categories Mechanical Engineering, Nonlinear Optimization, Nonsmooth Optimization Tags , , , ,

    Locally weighted regression combines the advantages of polynomial regression and kernel smoothing. We present three ideas for appropriate and effective use of LOcally WEighted Scatterplot Smoothing (LOWESS) models for surrogate optimization. First, a method is proposed to reduce the computational cost of LOWESS models. Second, a local scaling coefficient is introduced to adapt LOWESS models … Read more