A Certificate of Unboundedness for Polynomial Optimization Problems

Global polynomial optimization methods typically rely on compactness of the feasible region in order to find solutions. These methods can incur considerable computational expense and most commercially available solvers do not verify the existence of a solution prior to undergoing global search. In this manuscript we propose a simple pre-processing algorithm to determine if an arbitrary polynomial optimization problem is unbounded from below thereby providing information about the problem’s asymptotic geometry prior to solving the problem if a solution can be found.