A convex optimization approach to the covariance extension problem with degree constraint

We present an algorithm for solving the rational covariance extension problem with degree constraint. Given a partial covariance sequence and the desired zeros of the modeling filter, the poles are uniquely determined by the unique minimum of a convex optimization problem, which turns out to be the dual, in the sense of mathematical programming, of a problem to maximize a generalized entropy gain subject to linear constraints. This also provides a constructive proof of a long-standing conjecture of Georgiou (1983): Georgiou proved, by topological methods, that such poles always exist and conjectured that they are unique. In 1993 we proved a stronger version of this conjecture, but that proof was also nonconstructive