On convergence rate of a rectangular partition based global optimization algorithm

James Calvin, Gražina Gimbutienė, William O. Phillips, Antanas Žilinskas

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


The convergence rate of a rectangular partition based algorithm is considered. A hyper-rectangle for the subdivision is selected at each step according to a criterion rooted in the statistical models based theory of global optimization; only the objective function values are used to compute the criterion of selection. The convergence rate is analyzed assuming that the objective functions are twice- continuously differentiable and defined on the unit cube in d-dimensional Euclidean space. An asymptotic bound on the convergence rate is established. The results of numerical experiments are included.

Original languageEnglish (US)
Pages (from-to)165-191
Number of pages27
JournalJournal of Global Optimization
Issue number1
StatePublished - May 1 2018
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Control and Optimization
  • Applied Mathematics
  • Business, Management and Accounting (miscellaneous)
  • Computer Science Applications
  • Management Science and Operations Research


  • Bayesian approach
  • Convergence rate
  • Global optimization
  • P-algorithm
  • Rectangular partition
  • Statistical models for global optimization


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