This chapter extends the generalized disjunctive programming (GDP) model introduced in Chapter 7 to problems involved nonlinear objectives and nonlinear constraints. Relaxations of the GDP problem defined by the big-Mand hull reformulations are introduced, which can be used as a basis to reformulate the GDP problems as an MINLP. For the case of the hull reformulation, an approximation of the perspective function is presented that is exact for the 0-1 integer values. A disjunctive branch and bound method is described that can use as the relaxation the one of the big-M to the hull reformulation. Also, this chapter presents the logic-based outer-approximation method that can be used to solve GDP models for superstructure optimization of process flowsheets.
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