derivative-free optimization

Derivative-free methods for nonlinear programming with general lower-level constraints

  • Maria A. Diniz-Ehrhardt
  • José Mario Martínez
  • Lucas G. Pedroso
    • Categories Constrained Nonlinear Optimization Tags , , , , ,

    Augmented Lagrangian methods for derivative-free continuous optimization with constraints are introduced in this paper. The algorithms inherit the convergence results obtained by Andreani, Birgin, Martínez and Schuverdt for the case in which analytic derivatives exist and are available. In particular, feasible limit points satisfy KKT conditions under the Constant Positive Linear Dependence (CPLD) constraint qualification. … Read more

    Worst Case Complexity of Direct Search

  • Luis Nunes Vicente
    • Categories Nonlinear Optimization Tags , , ,

    In this paper we prove that direct search of directional type shares the worst case complexity bound of steepest descent when sufficient decrease is imposed using a quadratic function of the step size parameter. This result is proved under smoothness of the objective function and using a framework of the type of GSS (generating set … Read more

    Direct Multisearch for Multiobjective Optimization

  • Ana Luisa Custódio
  • A. Ismael F. Vaz
  • Luis Nunes Vicente
  • J. F. A. Madeira
    • Categories Multi-Criteria Optimization Tags , , , , , , ,

    In practical applications of optimization it is common to have several conflicting objective functions to optimize. Frequently, these functions are subject to noise or can be of black-box type, preventing the use of derivative-based techniques. We propose a novel multiobjective derivative-free methodology, calling it direct multisearch (DMS), which does not aggregate any of the objective … Read more

    Optimizing radial basis functions by D.C. programming and its use in direct search for global derivative-free optimization

  • Hoai An Le Thi
  • A. Ismael F. Vaz
  • Luis Nunes Vicente
    • Categories Global Optimization, Nonlinear Optimization Tags , , , , , ,

    In this paper we address the global optimization of functions subject to bound and linear constraints without using derivatives of the objective function. We investigate the use of derivative-free models based on radial basis functions (RBFs) in the search step of direct-search methods of directional type. We also study the application of algorithms based on … Read more

    A Derivative-Free Algorithm for the Least-square minimization

  • Andrew R. Conn
  • Katya Scheinberg
  • Hongchao Zhang
    • Categories Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , , , ,

    We develop a framework for a class of derivative-free algorithms for the least-squares minimization problem. These algorithms are based on polynomial interpolation models and are designed to take advantages of the problem structure. Under suitable conditions, we establish the global convergence and local quadratic convergence properties of these algorithms. Promising numerical results indicate the algorithm … Read more

    Self-correcting geometry in model-based algorithms for derivative-free unconstrained optimization

  • Katya Scheinberg
  • Philippe L. Toint
    • Categories Optimization of Simulated Systems, Unconstrained Optimization Tags , ,

    Several efficient methods for derivative-free optimization (DFO) are based on the construction and maintenance of an interpolation model for the objective function. Most of these algorithms use special “geometry-improving” iterations, where the geometry (poisedness) of the underlying interpolation set is made better at the cost of one or more function evaluations. We show that such … Read more

    Incorporating Minimum Frobenius Norm Models in Direct Search

  • Ana Luisa Custódio
  • Luis Nunes Vicente
  • Humberto Rocha
    • Categories Optimization Software Benchmark, Unconstrained Optimization Tags , , , , ,

    The goal of this paper is to show that the use of minimum Frobenius norm quadratic models can improve the performance of direct-search methods. The approach taken here is to maintain the structure of directional direct-search methods, organized around a search and a poll step, and to use the set of previously evaluated points generated … Read more

    PSwarm: A Hybrid Solver for Linearly Constrained Global Derivative-Free Optimization

  • A. Ismael F. Vaz
  • Luis Nunes Vicente
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Global Optimization Tags , , , , , , ,

    PSwarm was developed originally for the global optimization of functions without derivatives and where the variables are within upper and lower bounds. The underlying algorithm used is a pattern search method, more specifically a coordinate search method, which guarantees convergence to stationary points from arbitrary starting points. In the (optional) search step of coordinate search, … Read more

    Implicitely and Densely Discrete Black-Box Optimization Problems

  • Luis Nunes Vicente
    • Categories Integer Programming, Nonlinear Optimization, Other Topics Tags , , , , , ,

    This paper addresses derivative-free optimization problems where the variables lie implicitly in an unknown discrete closed set. The evaluation of the objective function follows a projection onto the discrete set, which is assumed dense rather than sparse. Such a mathematical setting is a rough representation of what is common in many real-life applications where, despite … Read more

    ORBIT: Optimization by Radial Basis Function Interpolation in Trust-Regions

  • Rommel Regis
  • Christine Shoemaker
  • Stefan M. Wild
    • Categories Optimization of Simulated Systems, Unconstrained Optimization Tags , , ,

    We present a new derivative-free algorithm, ORBIT, for unconstrained local optimization of computationally expensive functions. A trust-region framework using interpolating Radial Basis Function (RBF) models is employed. The RBF models considered often allow ORBIT to interpolate nonlinear functions using fewer function evaluations than the polynomial models considered by present techniques. Approximation guarantees are obtained by … Read more