Abstract
A computationally improved matrix-dilation approach is proposed for a robust semidefinite programming problem, whose constraint is a polynomial of uncertain parameters. This approach utilizes a sparse structure of the constraint polynomial and produces a small-size approximate problem to a given robust semidefinite programming problem. It is proved that the optimal value of the approximate problem converges to that of the given robust semidefinite programming problem as the used division of the parameter region becomes finer. In this sense, this approach is asymptotically exact. The size of the approximate problem is evaluated in the degree of the polynomial and is compared with the existing matrix-dilation approach. A numerical example is presented for illustration.
