Global optimization of non-convex generalized disjunctive programs: a review on reformulations and relaxation techniques

In this paper we present a review on the latest advances in logic-based solution methods for the global optimization of non-convex generalized disjunctive programs. Considering that the performance of these methods relies on the quality of the relaxations that can be generated, our focus is on the discussion of a general framework to find strong relaxations. We identify two main sources of non-convexities that any methodology to find relaxations should account for. Namely, the one arising from the non-convex functions and the one arising from the disjunctive set. We review the work that has been done on these two fronts with special emphasis on the latter. We then describe different logic-based optimization techniques that make use of the relaxation framework and its impact through a set of numerical examples typically encountered in Process Systems Engineering. Finally, we outline challenges and future lines of work in this area.

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