Multisection in Interval Branch-and-Bound Methods for Global Optimization I. Theoretical Results

András Erik Csallner, T. Csendes, Mihály Csaba Markót

Research output: Contribution to journalArticle

27 Citations (Scopus)

Abstract

We have investigated variants of interval branch-and-bound algorithms for global optimization where the bisection step was substituted by the subdivision of the current, actual interval into many subintervals in a single iteration step. The convergence properties of the multisplitting methods, an important class of multisection procedures are investigated in detail. We also studied theoretically the convergence improvements caused by multisection on algorithms which involve the accelerating tests (like e.g. the monotonicity test). The results are published in two papers, the second one contains the numerical test result.

Original languageEnglish
Pages (from-to)371-392
Number of pages22
JournalJournal of Global Optimization
Volume16
Issue number4
Publication statusPublished - Apr 2000

Fingerprint

Branch and bound method
Branch and Bound Method
Interval Methods
Global optimization
Global Optimization
Multisplitting
Interval
Bisection
Branch and Bound Algorithm
Subdivision
Convergence Properties
Monotonicity
Iteration
Branch-and-bound
test
method

Keywords

  • Accelerating devices
  • Branch-and-bound method
  • Global optimization
  • Interval arithmetic
  • Multisection

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Global and Planetary Change
  • Applied Mathematics
  • Control and Optimization

Cite this

Multisection in Interval Branch-and-Bound Methods for Global Optimization I. Theoretical Results. / Csallner, András Erik; Csendes, T.; Markót, Mihály Csaba.

In: Journal of Global Optimization, Vol. 16, No. 4, 04.2000, p. 371-392.

Research output: Contribution to journalArticle

Csallner, András Erik ; Csendes, T. ; Markót, Mihály Csaba. / Multisection in Interval Branch-and-Bound Methods for Global Optimization I. Theoretical Results. In: Journal of Global Optimization. 2000 ; Vol. 16, No. 4. pp. 371-392.
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