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GGOPT: an unconstrained non-linear optimizer.

J B Bassingthwaighte1, I S Chan, A A Goldstein

  • 1Center for Bioengineering, University of Washington, Seattle 98195.

Computer Methods and Programs in Biomedicine
|May 1, 1988
PubMed
Summary
This summary is machine-generated.

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GGOPT is a novel derivative-free optimizer designed for noisy smooth functions. It enhances parameter estimation accuracy by smoothing function values, gradients, and Hessians using an adjustable mesh and linear least squares.

Area of Science:

  • Numerical Analysis
  • Optimization Algorithms
  • Computational Mathematics

Background:

  • Non-linear optimization is crucial in many scientific and engineering fields.
  • Real-world function evaluations often contain noise from observations or computations, complicating optimization.
  • Existing derivative-free methods may struggle with noisy data, leading to inaccurate parameter estimates.

Purpose of the Study:

  • To introduce GGOPT, a derivative-free non-linear optimizer robust to noisy function evaluations.
  • To improve the accuracy of parameter estimation in the presence of significant function value errors.
  • To provide a method that effectively handles smooth functions with added noise.

Main Methods:

  • GGOPT employs an adjustable mesh strategy to locally approximate the function.

Related Experiment Videos

  • Linear least squares are utilized to compute smoothed function, gradient, and Hessian values at the mesh center.
  • A descent method, driven by these smoothed values, estimates the optimal parameters.

    • Main Results:

    • The smoothing process using an adjustable mesh and linear least squares effectively reduces the impact of noise.
    • Smoothed function, gradient, and Hessian estimates lead to more reliable parameter estimation.
    • The derivative-free approach makes GGOPT applicable to functions where derivatives are unavailable or difficult to compute.

    Conclusions:

    • GGOPT offers a robust and accurate solution for derivative-free non-linear optimization of noisy smooth functions.
    • The method's ability to provide smoothed derivative information enhances optimization performance.
    • This approach is particularly valuable when function values are derived from empirical data or computationally intensive simulations.