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In this paper, we develop new continuous and discrete relaxations fornonlinear expressions in an MINLP. In contrast to factorable programming, ourtechniques utilize the inner-function structure by encapsulating it in apolyhedral set, using a technique first proposed in [12]. We tighten therelaxations derived in [33,13] and obtain new relaxations for functions thatcould not be treated using prior techniques. We develop newdiscretization-based mixed-integer programming relaxations that yield tighterrelaxations than similar relaxations in the literature. These relaxationsutilize the simplotope that captures inner-function structure to generalize theincremental formulation of [8] to multivariate functions. In particular, whenthe outer-function is supermodular, our formulations require exponentiallyfewer continuous variables than any previously known formulation.

Extracting structure from functional expressions for continuous and discrete relaxations of MINLP