A convergent hierarchy of SDP relaxations for a class of hard robust global polynomial optimization problems

A hierarchy of semidefinite programming (SDP) relaxations is proposed for solving a broad class of hard nonconvex robust polynomial optimization problems under constraint data uncertainty, described by convex quadratic inequalities. This class of robust polynomial optimization problems, in general, does not admit exact semidefinite program reformulations. Convergence of the proposed SDP hierarchy is given under suitable and easily verifiable conditions. Known exact relaxation results are also deduced from the proposed scheme for the special class of robust convex quadratic programs. Numerical examples are provided, demonstrating the results.