 
Summary: 1
Structured Methods for Solving Hankel Matrix
Approximation Problems
Suliman AlHomidan
Department of Mathematical Sciences, King Fahd University of Petroleum and
Minerals, Dhahran 31261, PO Box 119, Saudi Arabia Email:
homidan@kfupm.edu.sa
Abstract
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.
Key words : Nonsmooth optimization, positive semidefinite matrix, Hankel matrix,
SQP Method, BFGS Method.
AMS (MOS) subject classifications; 65F99, 99C25, 65F30.
1 Introduction
