Journal of Global Optimization

, Volume 69, Issue 2, pp 283–307 | Cite as

Global optimization of disjunctive programs

  • Peter Kirst
  • Fabian Rigterink
  • Oliver Stein


We propose a new branch-and-bound framework for global optimization of disjunctive programs with general logical expressions. We do not assume the logical expressions to be in any normal form, and, under slightly stronger assumptions, we allow the use of negations and implications. In contrast to the widely used reformulation as a mixed-integer program, we compute the lower bounds and evaluate the logical expression in one step. Thus, we reduce the size of the problem and work exclusively with continuous variables, which is computationally advantageous. We present preliminary numerical results as proof of concept.


Global optimization Disjunctive programming Generalized disjunctive programming Branch-and-bound 

Mathematics Subject Classification

90C26 90C30 



We thank two anonymous referees for their precise and substantial remarks, which helped to significantly improve the paper.


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Institute of Operations ResearchKarlsruhe Institute of TechnologyKarlsruheGermany
  2. 2.School of Mathematical and Physical SciencesThe University of NewcastleNewcastleAustralia

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