A method for convex black-box integer global optimization

We study the problem of minimizing a convex function on nonempty, finite subset integer lattice when cannot be evaluated at noninteger points. propose new underestimator that does not require access to (sub)gradients objective; such information is unavailable objective blackbox function. Rather, our uses secant linear functions interpolate previously These mappings are shown underestimate in disconnected portions domain. Therefore, union these conditional cuts provides nonconvex objective. an algorithm alternates between updating and evaluating prove converges global minimum feasible set. present two approaches for representing compare their computational effectiveness. also implementations with existing methods lattice. discuss difficulty this class provide insights into why proof optimality challenging even moderate sizes.