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Derivative-Free Optimization Of Expensive Functions With Computational Error Using Weighted Regression
KTH, School of Electrical Engineering (EES), Automatic Control.
2013 (English)In: SIAM Journal on Optimization, ISSN 1052-6234, E-ISSN 1095-7189, Vol. 23, no 1, 27-53 p.Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
2013. Vol. 23, no 1, 27-53 p.
Keyword [en]
derivative-free optimization, weighted regression models, noisy function evaluations
National Category
Computational Mathematics
URN: urn:nbn:se:kth:diva-122132DOI: 10.1137/100814688ISI: 000316857500002ScopusID: 2-s2.0-84877763469OAI: diva2:621166

QC 20130514

Available from: 2013-05-14 Created: 2013-05-13 Last updated: 2014-01-20Bibliographically approved

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