A sequentially optimal randomized algorithm for robust LMI feasibility problems

This paper proposes a randomized algorithm for feasibility of uncertain LMIs. The algorithm is based on the solution of a sequence of semidefinite optimization problems involving a reduced number of constraints. A bound of the maximum number of iterations required by the algorithm is given. Analogies and differences with the gradient and localization methods are discussed. Finally, the performance and behaviour of the algorithm are illustrated by means of a numerical example.