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Semidefinite and second-order cone optimization approach for the Toeplitz matrix approximation problem. (English) Zbl 1096.65052
Summary: The nearest positive semidefinite symmetric Toeplitz matrix to an arbitrary data covariance matrix; is useful in many areas of engineering, including stochastic filtering and digital signal processing applications. In this paper, the interior point primal-dual path-following method will be used to solve our problem after reformulating it into different forms, first as a semidefinite programming problem, then into the form of a mixed semidefinite and second-order cone optimization problem. Numerical results, comparing the performance of these methods against the modified alternating projection method are reported.

MSC:
65K05 Numerical mathematical programming methods
90C20 Quadratic programming
90C22 Semidefinite programming
Software:
filterSQP; SDPA; SDPpack
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