Al-Homidan, Suliman S. SQP algorithms for solving Toeplitz matrix approximation problem. (English) Zbl 1071.65081 Numer. Linear Algebra Appl. 9, No. 8, 619-627 (2002). The following problem is considered: Given an \(n \times n\) matrix \(F\) and a natural number \(m \leq n\), find an \(n \times n\) symmetric positive semi-definite Toeplitz matrix \(T\) that minimizes the distance \(\| F-T \| \) in the Frobenius norm and whose rank is equal to \(m\). By means of a block \(LDL^{\text{T}}\) factorization of \(T\), the problem is reformulated, i.e., constraints put on \(T\) are transformed into a simpler form. Then, an SQP-based algorithm is presented and illustrated by numerical examples. Reviewer: Jan Chleboun (Praha) Cited in 3 Documents MSC: 65K05 Numerical mathematical programming methods 90C90 Applications of mathematical programming 90C55 Methods of successive quadratic programming type Keywords:filter SQP; non-smooth optimization; positive semi-definite matrix; Toeplitz matrix; \(l_1\) SQP method Software:filterSQP PDFBibTeX XMLCite \textit{S. S. Al-Homidan}, Numer. Linear Algebra Appl. 9, No. 8, 619--627 (2002; Zbl 1071.65081) Full Text: DOI References: [1] Kailath, IEEE Transactions on Information Theory IT-20 pp 145– (1974) [2] Cybenko, Circuits Systems Signal Processing 1 pp 345– (1982) [3] Digital Signal Processing and Control and Estimation Theory. MIT Press: Cambridge, MA, 1979. [4] Discrete Random Signals and Statistical Signal Processing. Prentice-Hall: Englewood Cliffs, NJ, 1992. · Zbl 0747.94004 [5] The jury test and covariance control. In Proceedings of the Symposium on Fundamentals of Discrete Time Systems, Chicago, 1992. [6] Fletcher, SIAM Journal on Control and Optimization 23 pp 493– (1985) [7] Practical Methods of Optimization. Wiley: Chichester, 1987. · Zbl 0905.65002 [8] Numerical experiments with an exact filter penalty function method. In Nonlinear Programming 4, (eds). Academic Press: New York, 1981. [9] User manual for filterSQP. Numerical Analysis Report, (NA/181), University of Dundee, 1999. [10] Suffridge, SIAM Journal on Matrix Analysis and Applications 14 pp 721– (1993) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.