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Derivative-free Optimization of Expensive Functions with Computational Error Using Weighted Regression

Stephen Billups (Stephen.Billups***at***ucdenver.edu)
Jeffrey Larson (Jeffrey.Larson***at***ucdenver.edu)
Peter Graf (Peter.Graf***at***nrel.gov)

Abstract: We propose a derivative-free algorithm for optimizing computationally expensive functions with computational error. The algorithm is based on the trust region regression method by Conn, Scheinberg, and Vicente [4], but uses weighted regression to obtain more accurate model functions at each trust region iteration. A heuristic weighting scheme is proposed which simultaneously handles i) differing levels of uncertainty in function evaluations, and ii) errors induced by poor model fidelity. We also extend the theory of Λ-poisedness and strong Λ-poisedness to weighted regression. We report computational results comparing interpolation, regression, and weighted regression methods on a collection of benchmark problems. Weighted regression appears to outperform interpolation and regression models on nondifferentiable functions and functions with deterministic noise.

Keywords: Derivative-Free Optimization, Lambda-poisedness, weighted regression models, trust region methods

Category 1: Nonlinear Optimization (Unconstrained Optimization )


Download: [Postscript]

Entry Submitted: 02/14/2011
Entry Accepted: 02/14/2011
Entry Last Modified: 02/20/2012

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