Intersection cuts have been tackled in recent years to tighten the polyhedral outer approximation of certain non-convex sets such as lattice set, bi-level set, outer product set and quadratic set. In this work, we study the intersection cuts for signomial set and mixed-integer-signomial set. Signomial Programs and Mixed-Integer Signomial Programs contain signomial terms, the intersection cuts can tighten their Linear Programming (LP) relaxations. 

The intersection cut framework requires two ingredients to generate a valid inequality: a translated simplicial conic relaxation and an S-free set. The spatial-branch-and-bound (sBB) algorithm is a general technique to find the global solution of non-convex MINLPs. the translated simplicial conic relaxation can be retrieved from the LP-based sBB algorithm. For S being signomial and mixed-integer-signomial sets, we give the construction of S-free sets. The intersection cut separation problem is reduced to univariate root-finding problems. Such root-finding problems can be solved numerically in quadratic convergence rate by Newton-like algorithms.