Abstract:

Our research focuses on mixed integer nonlinear programming problems (MINLP) in which all nonconvex functions are univariable and separable. We employ the Sequential Convex MINLP technique to solve this class of problems to obtain a global optimal solution. This method uses piecewise linear relaxation, where only the concave parts are replaced by linear functions. In contrast, the convex intervals are handled by generating cut planes using the perspective cuts. This work presents a comprehensive theoretical and computational analysis of the different possible reformulations to the original problem. We show and demonstrate that while they are equivalent in the case of purely linear problems, they are not equivalent when considering nonlinear convex intervals.