A recursive algorithm of exactness verification of relaxations for robust SDPs

This paper proposes a new computational method to verify the exactness of upper-bound relaxations for robust semidefinite programs. A recursive algorithm is provided that derives, from a dual optimal variable, a candidate of worst-case uncertainties that proves the exactness of an upper-bound relaxation. The algorithm is guaranteed to extract a set of true worst-case uncertainties if the dual optimal variable satisfies a rank condition, which relaxes the rank-one assumption in the previous methods. Numerical examples are provided to illustrate the algorithm that certifies exactness of upper-bound relaxations.