On solving MINLP problems with nonconvex signomials in SHOT

In this abstract, we briefly explain how the mixed-integer nonlinear programming solver SHOT is to be extended with a reformulation framework for nonconvex signomial functions. In the framework, nonconvex terms are convexified using lifting single-variable power and exponential transformations in combination with piecewise linear approximations. This gives a reformulated problem with a convex feasible region that overestimates that of the original nonconvex problem in an extended variable space. The reformulations are implemented using SHOT’s current reformulation functionality. Additionally, an updating mechanism is added to SHOT, which iteratively updates the piecewise linear approximations until the global optimal solution is found.