Christine Shoemaker

Global Convergence of Radial Basis Function Trust Region Derivative-Free Algorithms

  • Christine Shoemaker
  • Stefan M. Wild
    • Categories Civil and Environmental Engineering, Nonlinear Optimization, Unconstrained Optimization Tags , , ,

    We analyze globally convergent derivative-free trust region algorithms relying on radial basis function interpolation models. Our results extend the recent work of Conn, Scheinberg, and Vicente to fully linear models that have a nonlinear term. We characterize the types of radial basis functions that fit in our analysis and thus show global convergence to first-order … 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