, Volume 23, Issue 2, pp 591–616

Deterministic upper bounds for spatial branch-and-bound methods in global minimization with nonconvex constraints

Original Paper

DOI: 10.1007/s11750-015-0387-7

Cite this article as:
Kirst, P., Stein, O. & Steuermann, P. TOP (2015) 23: 591. doi:10.1007/s11750-015-0387-7


We discuss some difficulties in determining valid upper bounds in spatial branch-and-bound methods for global minimization in the presence of nonconvex constraints. In fact, two examples illustrate that standard techniques for the construction of upper bounds may fail in this setting. Instead, we propose to perturb infeasible iterates along Mangasarian–Fromovitz directions to feasible points whose objective function values serve as upper bounds. These directions may be calculated by the solution of a single linear optimization problem per iteration. Preliminary numerical results indicate that our enhanced algorithm solves optimization problems where a standard branch-and-bound method does not converge to the correct optimal value.


Branch-and-bound Convergence Consistency  Mangasarian–Fromovitz constraint qualification 

Mathematics Subject Classification


Copyright information

© Sociedad de Estadística e Investigación Operativa 2015

Authors and Affiliations

  1. 1.Institute of Operations ResearchKarlsruhe Institute of Technology (KIT)KarlsruheGermany
  2. 2.JüchenGermany

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