  Cutting planes are of crucial importance when solving nonconvex nonlinear
programs to global optimality, for example using the spatial branch-and-bound
algorithms. In this paper, we discuss the generation of cutting planes for
signomial programming. Many global optimization algorithms lift signomial
programs into an extended formulation such that these algorithms can construct
relaxations of the signomial program by outer approximations of the lifted set
encoding nonconvex signomial term sets, i.e., hypographs, or epigraphs of
signomial terms. We show that any signomial term set can be transformed into
the subset of the difference of two concave power functions, from which we
derive two kinds of valid linear inequalities. Intersection cuts are
constructed using signomial term-free sets which do not contain any point of
the signomial term set in their interior. We show that these signomial
term-free sets are maximal in the nonnegative orthant, and use them to derive
intersection sets. We then convexify a concave power function in the
reformulation of the signomial term set, resulting in a convex set containing
the signomial term set. This convex outer approximation is constructed in an
extended space, and we separate a class of valid linear inequalities by
projection from this approximation. We implement the valid inequalities in a
global optimization solver and test them on MINLPLib instances. Our results
show that both types of valid inequalities provide comparable reductions in
running time, number of search nodes, and duality gap.
