An interval method for bounding level sets of parameter estimation problems
type: Item
instance of: scholarly article
title: An interval method for bounding level sets of parameter estimation problems
zbMATH Open document ID: 0665.65099
DOI: 10.1007/BF02238730
published in: Computing
publication date: 1989-01-01T00:00:00Z
review text: The author examines the parameter estimation problem with objective function of sum-of-squares type: \(\min_{x\in X}f(x)=\sum^{m}_{i=1}(f_ i-f(i,x))^ 2\) where \(f_ i\) and f(i,x), \(i=1,2,...,m\) scalar functions of one and \(m+1\) arguments, respectively, and \(X=\{x\in {\mathbb{R}}^ n:\) \(a_ i\leq x_ i\leq b_ i\); \(a_ i,b_ i\in {\mathbb{R}}\), \(i=1,2,...,n\}\). The paper presents an algorithm that determines a bounding box by means of inclusion functions of the objective function and its gradient. The rate of convergence is studied, and cases when it is linear, superlinear or higher are shown. Examples examined prove that this algorithm sometimes can be used for nonlinear functions of more general form (not only those of least-squares form).
Mathematics Subject Classification ID: 65C99
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 62H12
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 4088893
zbMATH Keywords: interval method
zbMATH Keywords: level set
zbMATH Keywords: interval arithmetic
zbMATH Keywords: parameter estimation
zbMATH Keywords: inclusion functions
zbMATH Keywords: rate of convergence
author: Tibor Csendes
MaRDI profile type: Publication
cites work: FORTRAN-SC. A study of a FORTRAN extension for engineering/scientific computation with access to ACRITH
cites work: Q3801355
cites work: Properties of interval operators
cites work: Q3826105
cites work: Q3707258
cites work: Inclusion functions and global optimization
full work available at URL: https://doi.org/10.1007/bf02238730
OpenAlex ID: W1512968084
description: scientific article; zbMATH DE number 4088893