Journal of Global Optimization

, Volume 75, Issue 3, pp 595–629 | Cite as

A joint decomposition method for global optimization of multiscenario nonconvex mixed-integer nonlinear programs

  • Emmanuel Ogbe
  • Xiang LiEmail author


This paper proposes a joint decomposition method that combines Lagrangian decomposition and generalized Benders decomposition, to efficiently solve multiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems to global optimality, without the need for explicit branch and bound search. In this approach, we view the variables coupling the scenario dependent variables and those causing nonconvexity as complicating variables. We systematically solve the Lagrangian decomposition subproblems and the generalized Benders decomposition subproblems in a unified framework. The method requires the solution of a difficult relaxed master problem, but the problem is only solved when necessary. Enhancements to the method are made to reduce the number of the relaxed master problems to be solved and ease the solution of each relaxed master problem. We consider two scenario-based, two-stage stochastic nonconvex MINLP problems that arise from integrated design and operation of process networks in the case study, and we show that the proposed method can solve the two problems significantly faster than state-of-the-art global optimization solvers.


Generalized Benders decomposition Dantzig–Wolfe decomposition Lagrangian decomposition Joint decomposition Mixed-integer nonlinear programming Global optimization Stochastic programming 



The authors are grateful to the discovery grant (RGPIN 418411-13) and the collaborative research and development grant (CRDPJ 485798-15) from Natural Sciences and Engineering Research Council of Canada (NSERC).


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Chemical EngineeringQueen’s UniversityKingstonCanada

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