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This paper proposes a joint decomposition method that combines La- grangiandecomposition and generalized Benders decomposition, to efficiently solvemultiscenario nonconvex mixed-integer nonlinear programming (MINLP) problems toglobal optimality, without the need for explicit branch and bound search. Inthis approach, we view the variables coupling the scenario dependent variablesand those causing nonconvexity as complicating variables. We systemat- icallysolve the Lagrangian decomposition subproblems and the generalized Ben- dersdecomposition subproblems in a unified framework. The method requires thesolution of a difficult relaxed master problem, but the problem is only solvedwhen necessary. Enhancements to the method are made to reduce the number of therelaxed master problems to be solved and ease the solution of each relaxedmaster problem. We consider two scenario-based, two-stage stochastic nonconvexMINLP problems that arise from integrated design and operation of process net-works in the case study, and we show that the proposed method can solve the twoproblems significantly faster than state-of-the-art global optimizationsolvers.

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