Granularity for Mixed-Integer Polynomial Optimization Problems

Finding good feasible points is crucial in mixed-integer programming. For this purpose
we combine a sufficient condition for consistency, called granularity, with the moment-
/sum-of-squares-hierarchy from polynomial optimization. If the mixed-integer prob-
lem is granular, we obtain feasible points by solving continuous polynomial problems
and rounding their optimal points. The moment-/sum-of-squares-hierarchy is hereby
used to solve those continuous polynomial problems, which generalizes known meth-
ods from the literature. Numerical examples from the MINLPLib illustrate our
approach.