Polynomial Optimization on Some Unbounded Closed Semi-algebraic Sets

The article presents a study on a class of polynomial optimization problems over (noncompact) semi-algebraic sets which, by making changes of variables via suitable monomial mappings, become polynomial optimization problems over compact semi-algebraic feasible sets. It is known that the polynomial optimization problems on semi-algebraic feasible sets are satisfactory when the feasible sets are compact. Furthermore, determining whether a polynomial is bounded on such a semi-algebraic set can be replaced by checking whether its support lies in a closed and convex cone corresponding to the semi-algebraic set.