Draft: Global Optimization of Mixed-integer Nonlinear Systems Using Decomposition and Lagrangian Branch-and-cut

The analytical target cascading (ATC) optimization technique for hierarchical systems demonstrates convergence properties only under assumptions of convexity and continuity. Many practical engineering design problems, however, involve a combination of continuous and discrete variables resulting in the development of mixed integer nonlinear programming (MINLP) formulations. While ATC has been applied to solve MINLP problems, convergence and global optimality are not guaranteed. In this paper, we exploit the large-scale, decomposable structures of certain nonconvex MINLP models by adopting a Lagrangian based branch-and-cut algorithm in the ATC context to solve these models to global optimality. It is shown that the Lagrangian based branch-and-cut format fits into the Lagrangian motivated ATC framework, and is implemented using ATC notation. The resulting deterministic global optimization methodology is illustrated through the optimization of the joint product family platform selection and design problem from literature.