Journal of Global Optimization

, Volume 61, Issue 2, pp 203–220 | Cite as

A convergent conical algorithm with \(\omega \)-bisection for concave minimization

  • Takahito KunoEmail author
  • Tomohiro Ishihama


The conical algorithm is a global optimization algorithm proposed by Tuy in 1964 to solve concave minimization problems. Introducing the concept of pseudo-nonsingularity, we give an alternative proof of convergence of the algorithm with the \(\omega \)-subdivision rule. We also develop a new convergent subdivision rule, named \(\omega \)-bisection, and report numerical results of comparing it with the usual \(\omega \)-subdivision.


Global optimization Concave minimization Conical algorithm Bisection \(\omega \)-subdivision 



The authors would like to thank the anonymous referee for his/her valuable comments, which significantly improved the quality of this article.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Graduate School of Systems and Information EngineeringUniversity of TsukubaTsukubaJapan

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