noisy optimization

Optimistic Noise-Aware Sequential Quadratic Programming for Equality Constrained Optimization with Rank-Deficient Jacobians

  • Jiahao Shi
  • Baoyu Zhou
  • Albert S. Berahas
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization Tags , , , , , ,

    We propose and analyze a sequential quadratic programming algorithm for minimizing a noisy nonlinear smooth function subject to noisy nonlinear smooth equality constraints. The algorithm uses a step decomposition strategy and, as a result, is robust to potential rank-deficiency in the constraints, allows for two different step size strategies, and has an early stopping mechanism. … Read more

    An Interior-Point Algorithm for Continuous Nonlinearly Constrained Optimization with Noisy Function and Derivative Evaluations

  • Frank E. Curtis
  • Shima Dezfulian
  • Andreas Wächter
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Optimization of Simulated Systems Tags , , , ,

    An algorithm based on the interior-point methodology for solving continuous nonlinearly constrained optimization problems is proposed, analyzed, and tested. The distinguishing feature of the algorithm is that it presumes that only noisy values of the objective and constraint functions and their first-order derivatives are available. The algorithm is based on a combination of a previously … Read more

    A Trust Region Method for the Optimization of Noisy Functions

  • Shigeng Sun
  • Jorge Nocedal
    • Categories Nonlinear Optimization Tags , ,

    Classical trust region methods were designed to solve problems in which function and gradient information are exact. This paper considers the case when there are bounded errors (or noise) in the above computations and proposes a simple modification of the trust region method to cope with these errors. The new algorithm only requires information about … Read more

    Adaptive Finite-Difference Interval Estimation for Noisy Derivative-Free Optimization

  • Hao-Jun Shi
  • Yuchen Xie
  • Melody Xuan
  • Jorge Nocedal
    • Categories Nonlinear Optimization Tags , , , ,

    A common approach for minimizing a smooth nonlinear function is to employ finite-difference approximations to the gradient. While this can be easily performed when no error is present within the function evaluations, when the function is noisy, the optimal choice requires information about the noise level and higher-order derivatives of the function, which is often … Read more

    On the Numerical Performance of Derivative-Free Optimization Methods Based on Finite-Difference Approximations

  • Jorge Nocedal
  • Hao-Jun Shi
  • Melody Xuan
  • Figen Oztoprak
    • Categories Nonlinear Optimization Tags , , , ,

    The goal of this paper is to investigate an approach for derivative-free optimization that has not received sufficient attention in the literature and is yet one of the simplest to implement and parallelize. It consists of computing gradients of a smoothed approximation of the objective function (and constraints), and employing them within established codes. These … Read more

    A Noise-Tolerant Quasi-Newton Method for Unconstrained Optimization

  • Richard H. Byrd
  • Jorge Nocedal
  • Hao-Jun Shi
  • Yuchen Xie
    • Categories Unconstrained Optimization Tags , , ,

    This paper describes an extension of the BFGS and L-BFGS methods for the minimization of a nonlinear function subject to errors. This work is motivated by applications that contain computational noise, employ low-precision arithmetic, or are subject to statistical noise. The classical BFGS and L-BFGS methods can fail in such circumstances because the updating procedure … Read more