The impelling function method applied to global optimization
type: Item
instance of: scholarly article
title: The impelling function method applied to global optimization
zbMATH Open document ID: 1055.65077
DOI: 10.1016/S0096-3003(03)00525-3
author: Xian Liu
published in: Applied Mathematics and Computation
publication date: 2004-08-06T00:00:00Z
review text: The author considers a global constrained oprimization problem such as the following \[ \text{Glob.Min} \,f(X),\quad\text{subject to }g(X)\geq 0. \] He first uses the penalty function method (PFM) for transforming this problem into an unconstrained optimization problem where he sets \[ F(X,r)= f(X)+ r \sum^m_{i=1} \{\min(0, g_i(X))\}^2, \] \(r\geq 0\) is a penalty factor. Then the PFM concept is extended to global optimization. An auxiliary function \(M(X)\) is proposed such that it decreases in the region \(G(X)\underset{\text{def}}{}= \{X/f(X)\geq f(X_1)\}\) where \(X_1\) is the known best local minimizer and has a stationary point in \(\{X/f(X)< f(X_1)\}\). For instance the paper suggests the impelling function \[ M(X)= a\{\min[0, f(X)- f(X_1)]\}^{2m}-\| X- X_1\|^p, \] where \(m\) and \(p\) are positive natural numbers (partically \(m= 1\), \(p= 2\)). The following of this interesting paper gives theoretical results for convergence towards a global minimum.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 2082087
zbMATH Keywords: global optimization
zbMATH Keywords: penalty method
zbMATH Keywords: impelling function
zbMATH Keywords: Barrier function method
zbMATH Keywords: filled function method
zbMATH Keywords: minimization
zbMATH Keywords: nonlinear programming
reviewed by: Yves Cherruault
describes a project that uses: Global Optimization Toolbox For Maple
MaRDI profile type: Publication
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full work available at URL: s0096-3003(03)00525-3
OpenAlex ID: W2090160475
description: scientific article; zbMATH DE number 2082087