DERIVATIVE-FREE OPTIMIZATION OF EXPENSIVE FUNCTIONS WITH COMPUTATIONAL ERROR USING WEIGHTED REGRESSION

作者：Billups Stephen C^*; Larson Jeffrey; Graf Peter

来源：SIAM Journal on Optimization, 2013, 23(1): 27-53.

DOI：10.1137/100814688

• derivative-free optimization
• weighted regression models
• noisy function evaluations

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 [A. R. Conn, K. Scheinberg, and L. N. Vicente, IMA J. Numer. Anal., 28 (2008), pp. 721-748] but uses weighted regression to obtain more accurate model functions at each trust region iteration. A heuristic weighting scheme is proposed that simultaneously handles (i) differing levels of uncertainty in function evaluations and (ii) errors induced by poor model fidelity. We also extend the theory of Lambda-poisedness and strong Lambda-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.

• 出版日期2013