1Structured Methods for Solving Hankel Matrix Approximation Problems

The problem of finding the nearest positive semidefinite Hankel matrix of a given rank to an arbitrary matrix is considered. The problem is formulated as a nonlinear minimization problem with positive semidefinite Hankel matrix as constraints. Then an algorithm with rapid convergence is obtained by the Sequential Quadratic Programming (SQP) method. A second approach is to formulate the problem as a smooth unconstrained minimization problem, for which rapid convergence can be obtained by, for example, the BFGS method. This paper studies both methods. Comparative numerical results are reported