caa a22 4500 46316959X CHVBK 20180406164809.0 cr unu---uuuuu 170326e20071201xx s 000 0 eng 10.1007/s10957-007-9254-5 doi (NATIONALLICENCE)springer-10.1007/s10957-007-9254-5 Al-Homidan S. Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia aut Approximate Toeplitz Matrix Problem Using Semidefinite Programming [Elektronische Daten] [S. Al-Homidan] Given a data matrix, we find its nearest symmetric positive-semidefinite Toeplitz matrix. In this paper, we formulate the problem as an optimization problem with a quadratic objective function and semidefinite constraints. In particular, instead of solving the so-called normal equations, our algorithm eliminates the linear feasibility equations from the start to maintain exact primal and dual feasibility during the course of the algorithm. Subsequently, the search direction is found using an inexact Gauss-Newton method rather than a Newton method on a symmetrized system and is computed using a diagonal preconditioned conjugate-gradient-type method. Computational results illustrate the robustness of the algorithm. Springer Science+Business Media, LLC, 2007 Primal-dual interior-point methods nationallicence Projection methods nationallicence Toeplitz matrices nationallicence Semidefinite programming nationallicence Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 135/3(2007-12-01), 583-598 0022-3239 135:3<583 2007 135 10957 https://doi.org/10.1007/s10957-007-9254-5 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10957-007-9254-5 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Al-Homidan S. Department of Mathematical Sciences, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia aut NATIONALLICENCE 773 0- Journal of Optimization Theory and Applications Springer US; http://www.springer-ny.com 135/3(2007-12-01), 583-598 0022-3239 135:3<583 2007 135 10957 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer