On the use of restriction of the right-hand side in spatial branch-and-bound algorithms to ensure termination

Peter Kirst () and Christian Füllner ()
Additional contact information
Peter Kirst: Wageningen University & Research (WUR)
Christian Füllner: Karlsruhe Institute of Technology

Computational Optimization and Applications, 2025, vol. 90, issue 3, No 4, 720 pages

Abstract: Abstract Spatial branch-and-bound algorithms for global minimization of non-convex problems require both lower and upper bounding procedures that finally converge to a globally optimal value in order to ensure termination of these methods. Whereas convergence of lower bounds is commonly guaranteed for standard approaches in the literature, this does not always hold for upper bounds. For this reason, different so-called convergent upper bounding procedures are proposed. These methods are not always used in practice, possibly due to their additional complexity or possibly due to increasing runtimes on average problems. For that reason, in this article we propose a refinement of classical branch-and-bound methods that is simple to implement and comes with marginal overhead. We prove that this small improvement already leads to convergent upper bounds, and thus show that termination of spatial branch-and-bound methods is ensured under mild assumptions.

Keywords: global optimization; branch-and-bound; upper bounding procedure; feasible points; feasibility verification; restriction of the right-hand side; 90C26 (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10589-025-00652-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:coopap:v:90:y:2025:i:3:d:10.1007_s10589-025-00652-5

Ordering information: This journal article can be ordered from
http://www.springer.com/math/journal/10589

DOI: 10.1007/s10589-025-00652-5

Access Statistics for this article

Computational Optimization and Applications is currently edited by William W. Hager

More articles in Computational Optimization and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().