Computing optimality certificates for convex mixed-integer nonlinear problems - Halbig, Katrin; Hümbs, Lukas; Rösel, Florian; Schewe, Lars; Weninger, Dieter (2021)
Every optimization problem has a corresponding verification problem which verifies whether a given optimal solution is in fact optimal. In the literature there are a lot of such ways to verify optimality for a given solution, e.g., the branch-and-bound tree. To simplify this task, Baes et al. introduced optimality certificates for convex mixed-integer nonlinear programs and proved that these are bounded in the number of integer variables. We introduce an algorithm to compute the certificates and conduct computational experiments. Through the experiments we show that the optimality certificates can be surprisingly small.<br
Keywords: Mixed-integer optimization; Mixed-integer convex optimization