Spline and weighted random directions method for nonlinear optimization
type: Item
instance of: scholarly article
title: Spline and weighted random directions method for nonlinear optimization
zbMATH Open document ID: 0579.65064
DOI: 10.1016/0025-5564(85)90058-6
author: B. George
published in: Mathematical Biosciences
publication date: 1985-01-01T00:00:00Z
review text: For the unconstrained minimization problem \(\min \{F(x)| x\in {\mathbb{R}}^ n\}\) the following method is proposed: A random basis is generated and orthogonalized by the Gram-Schmidt algorithm to yield \(v_ 1,...,v_ n\). These directions are weighted to yield final search directions \(w_ i=W_ iv_ i\) with \(W_ i=diag(p_ 1,...,p_ n)\), \(p_ j=(x_ j^{(i)})^{-1/2}\) if \(x_ j^{(i)}>0\) and (for unknown reasons) simply \(p_ j=1\) if \(x_ j^{(i)}\leq 0\). In each direction of search 5 equidistant points are determined and a line search is based on either a cubic spline interpolate or a fourth degree interpolation polynomial. The algorithm does not become clear in all details from the paper. A proof of convergence or order of convergence is not given. Numerous numerical examples say little about the algorithm as they are not sufficiently documented (starting points, accuracy obtained) or compared with other algorithms. A reported number of 2310 function evaluations to minimize the 2-dimensional Rosenbrock function give little hope for a high efficiency.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 3928233
zbMATH Keywords: descent methods
zbMATH Keywords: unconstrained minimization
zbMATH Keywords: Gram-Schmidt algorithm
zbMATH Keywords: line search
zbMATH Keywords: fourth degree interpolation
zbMATH Keywords: numerical examples
MaRDI profile type: Publication
full work available at URL: 0025-5564(85)90058-6
OpenAlex ID: W1999943989
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description: scientific article; zbMATH DE number 3928233