Title: Computing Optimality Certificates for Convex Mixed-Integer Nonlinear Problems

Abstract: Every optimization problem has a corresponding verification
problem that checks 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, for example, the branch-and-bound tree. To simplify this task, optimality certificates were introduced for convex mixed-integernonlinear programs, and it was shown that the sizes of the certificates are bounded in terms of 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.