An interval algorithm for constrained global optimization
type: Item
instance of: scholarly article
title: An interval algorithm for constrained global optimization
zbMATH Open document ID: 0809.65064
DOI: 10.1016/0377-0427(94)90331-X
published in: Journal of Computational and Applied Mathematics
publication date: 1994-09-22T00:00:00Z
review text: An interval arithmetic method for solving the global constrained problem \(\min f(x)\), \(g(x)= 0\), \(h(x)\leq 0\) is presented which shows the following features: (i) The problem is transformed to a penalty approach, \(\min F(x)\) with \(F= f+ cp\) and \(c\) being the penalty factor and \(p\) the \(L_ 1\)-exact penalty term. (ii) Numerical experience and computational results suggest the choice of a factor \(c\geq \bar c\), where \(\bar c= O(\max| f(x)|)\). Then the computation is rather insensitive to changes of \(c\). However, the value of \(\bar c\) has not been exploited completely yet. (iii) Additionally, infeasible areas \(Y\) are discarded during the computation using appropriate interval arithmetic exclusion tests.
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 65G30
Mathematics Subject Classification ID: 90C30
zbMATH DE Number: 643786
zbMATH Keywords: constrained global optimization
zbMATH Keywords: penalty function
zbMATH Keywords: numerical experience
zbMATH Keywords: interval arithmetic
zbMATH Keywords: computational results
author: Michael A. Wolfe
reviewed by: H. Ratschek
MaRDI profile type: Publication
cites work: Q3345690
cites work: Q5589755
cites work: Q4404674
cites work: Augmentability in optimization theory
cites work: Q3207999
cites work: Q3796646
cites work: Derived eigenvalues of symmetric matrices, with applications to distance geometry
cites work: Q4040272
cites work: On interval enclosures using slope arithmetic
description: scientific article; zbMATH DE number 643786