(Three) Cutting Planes for Signomial Programming


The generation of cutting planes is crucial in solving non-convex Mixed-Integer Nonlinear Programming problems to $\epsilon$-global optimality. In this work, we study the signomial-term set (the graph of a signomial term function) arising in the extended formulation of Signomial Programming, and we show that it suffices to consider the signomial-term set as the epigraph/hypograph of the associated signomial term function. We present a useful reformulation of the signomial-term set, written as the zero-sublevel set of the difference of two concave power functions. We propose three types of valid linear inequalities: intersection cuts and two types of outer approximation cuts. slides

This talk is presented at session XV. Workshop on Global Optimization (HUGO2022).