UOBYQA: unconstrained optimization by quadratic approximation
type: Item
instance of: scholarly article
title: UOBYQA: unconstrained optimization by quadratic approximation
zbMATH Open document ID: 1014.65050
author: M. J. D. Powell
published in: Mathematical Programming. Series A. Series B
publication date: 2002-12-01T00:00:00Z
full work available at URL: http://citeseerx.ist.psu.edu/viewdoc/summary
review text: A new algorithm for general unconstrained optimization calculations is described. It takes account of the curvature of the objective function by forming quadratic models by interpolation. Obviously, no first derivatives are required. A typical iteration of the algorithm generates a new vector of variables either by minimizing the quadratic model subject to a trust region bound, or by a procedure that should improve the accuracy of the model. The paper addresses the initial positions of the interpolation points and the adjustment of trust region radii. The algorithm works with the Lagrange functions of the interpolation equations explicitly; therefore their coefficients are updated when an interpolation point is moved. The Lagrange functions assist the procedure that improves the model and also they provide an estimate of the error of the quadratic approximation of the function being minimized. It is pointed out that results are very promising for functions with less than twenty variables.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 90C56
zbMATH DE Number: 1837129
zbMATH Keywords: unconstrained optimization
zbMATH Keywords: quadratic approximation
zbMATH Keywords: trust region method
zbMATH Keywords: error bounds
zbMATH Keywords: algorithm
reviewed by: R. P. Tewarson
describes a project that uses: DFO
describes a project that uses: GQTPAR
MaRDI profile type: Publication
OpenAlex ID: W2163913714
DOI: 10.1007/S101070100290
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description: scientific article; zbMATH DE number 1837129