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

Emmanuel Ogbe and Xiang Li ()
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Emmanuel Ogbe: Queen’s University
Xiang Li: Queen’s University

Journal of Global Optimization, 2019, vol. 75, issue 3, No 2, 595-629

Abstract: Abstract 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.

Keywords: Generalized Benders decomposition; Dantzig–Wolfe decomposition; Lagrangian decomposition; Joint decomposition; Mixed-integer nonlinear programming; Global optimization; Stochastic programming (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10898-019-00786-x

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