Semidefinite and second-order cone optimization approach for the Toeplitz matrix approximation problem

The nearest positive semidefinite symmetric Toeplitz matrix to an arbitrary data covariance matrix is useful in many areas of engineering, including stochastic filtering and digital signal processing applications. In this paper, the interior point primal-dual path-following method will be used to solve our problem after reformulating it into different forms, first as a semidefinite programming problem, then into the form of a mixed semidefinite and second-order cone optimization problem. Numerical results, comparing the performance of these methods against the modified alternating projection method will be reported.