 
Summary: 1
SQP Algorithms for Solving Toeplitz Matrix
Approximation Problem
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
Given an n×n matrix F, we find the nearest symmetric positive semidefinite
Toeplitz matrix T to F. The problem is formulated as a nonlinear minimization
problem with positive semidefinite Toeplitz matrix as constraints. Then a
computational framework is given. An algorithm with rapid convergence is
obtained by l1Sequential Quadratic Programming (SQP) method.
Key words : nonsmooth optimization, positive semidefinite matrix, Toeplitz ma
trix, SQP method, l1SQP Method.
AMS (MOS) subject classifications 65F99, 99C25, 65F30
1 Introduction
The problem we are interested in is the best approximation of a given matrix by a
positive semidefinite symmetric Toeplitz matrix. Toeplitz matrices appear naturally
in a variety of problems in engineering. Since positive semidefinite Toeplitz matrices
