Subdivision Direction Selection in Interval Methods for Global Optimization

T. Csendes, D. Ratz

Research output: Contribution to journalArticle

90 Citations (Scopus)

Abstract

The role of the interval subdivision-selection rule is investigated in branch-and-bound algorithms for global optimization. The class of rules that allows convergence for the model algorithm is characterized, and it is shown that the four rules investigated satisfy the conditions of convergence. A numerical study with a wide spectrum of test problems indicates that there are substantial differences between the rules in terms of the required CPU time, the number of function and derivative evaluations, and space complexity, and two rules can provide substantial improvements in efficiency.

Original languageEnglish
Pages (from-to)922-938
Number of pages17
JournalSIAM Journal on Numerical Analysis
Volume34
Issue number3
Publication statusPublished - 1997

Fingerprint

Interval Methods
Global optimization
Subdivision
Global Optimization
Program processors
Derivatives
Selection Rules
Space Complexity
Branch and Bound Algorithm
CPU Time
Test Problems
Numerical Study
Derivative
Interval
Evaluation

Keywords

  • Global optimization
  • Interval arithmetic
  • Interval subdivision

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Computational Mathematics

Cite this

Subdivision Direction Selection in Interval Methods for Global Optimization. / Csendes, T.; Ratz, D.

In: SIAM Journal on Numerical Analysis, Vol. 34, No. 3, 1997, p. 922-938.

Research output: Contribution to journalArticle

@article{5a9d38d5a544413c9efba3baef0400a6,
title = "Subdivision Direction Selection in Interval Methods for Global Optimization",
abstract = "The role of the interval subdivision-selection rule is investigated in branch-and-bound algorithms for global optimization. The class of rules that allows convergence for the model algorithm is characterized, and it is shown that the four rules investigated satisfy the conditions of convergence. A numerical study with a wide spectrum of test problems indicates that there are substantial differences between the rules in terms of the required CPU time, the number of function and derivative evaluations, and space complexity, and two rules can provide substantial improvements in efficiency.",
keywords = "Global optimization, Interval arithmetic, Interval subdivision",
author = "T. Csendes and D. Ratz",
year = "1997",
language = "English",
volume = "34",
pages = "922--938",
journal = "SIAM Journal on Numerical Analysis",
issn = "0036-1429",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "3",

}

TY - JOUR

T1 - Subdivision Direction Selection in Interval Methods for Global Optimization

AU - Csendes, T.

AU - Ratz, D.

PY - 1997

Y1 - 1997

N2 - The role of the interval subdivision-selection rule is investigated in branch-and-bound algorithms for global optimization. The class of rules that allows convergence for the model algorithm is characterized, and it is shown that the four rules investigated satisfy the conditions of convergence. A numerical study with a wide spectrum of test problems indicates that there are substantial differences between the rules in terms of the required CPU time, the number of function and derivative evaluations, and space complexity, and two rules can provide substantial improvements in efficiency.

AB - The role of the interval subdivision-selection rule is investigated in branch-and-bound algorithms for global optimization. The class of rules that allows convergence for the model algorithm is characterized, and it is shown that the four rules investigated satisfy the conditions of convergence. A numerical study with a wide spectrum of test problems indicates that there are substantial differences between the rules in terms of the required CPU time, the number of function and derivative evaluations, and space complexity, and two rules can provide substantial improvements in efficiency.

KW - Global optimization

KW - Interval arithmetic

KW - Interval subdivision

UR - http://www.scopus.com/inward/record.url?scp=0000064119&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000064119&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0000064119

VL - 34

SP - 922

EP - 938

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

SN - 0036-1429

IS - 3

ER -