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SQP algorithms for solving Toeplitz matrix approximation problem. (English) Zbl 1071.65081
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.

##### MSC:
 65K05 Numerical mathematical programming methods 90C90 Applications of mathematical programming 90C55 Methods of successive quadratic programming type
filterSQP
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##### References:
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