Unconstrained derivative-free optimization by successive approximation
type: Item
instance of: scholarly article
title: Unconstrained derivative-free optimization by successive approximation
zbMATH Open document ID: 1155.65044
author: Árpád Bűrmen
author: Tadej Tuma
published in: Journal of Computational and Applied Mathematics
publication date: 2008-11-20T00:00:00Z
review text: The authors present an algorithmic framework for unconstrained derivative-free optimization based on successive approximation. The framework relies on the grid restrainment and search space partitioning to ensure that a subsequence of iterates exists that converges to a local minimizer of a continuously differentiable function. Its convergence is established under mild assumptions. A variant of the Nelder-Mead algorithm conforming to the framework is described. The algorithm is tested on the Moré-Garbow-Hillstrom test suite and on some multi-dimensional test problems with dimension ranging up to 100. The results showed that the proposed algorithm outperforms two previously known convergent simplex variants.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C56
zbMATH DE Number: 5370018
zbMATH Keywords: direct search
zbMATH Keywords: successive approximation
zbMATH Keywords: grid
zbMATH Keywords: simplex
zbMATH Keywords: numerical examples
zbMATH Keywords: unconstrained derivative-free optimization
zbMATH Keywords: convergence
zbMATH Keywords: Nelder-Mead algorithm
zbMATH Keywords: Moré-Garbow-Hillstrom test suite
describes a project that uses: minpack
describes a project that uses: fminsearch
MaRDI profile type: Publication
full work available at URL: j.cam.2007.12.017
OpenAlex ID: W2140622762
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DOI: 10.1016/J.CAM.2007.12.017
description: scientific article; zbMATH DE number 5370018