On the low rank solution of the Q‐weighted nearest correlation matrix problem |
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| Authors: | Xue‐Feng Duan Jian‐Chao Bai Jiao‐Fen Li Jing‐Jing Peng |
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| Affiliation: | 1. College of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin, China;2. School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, China;3. College of Mathematics and Econometrics, Hunan University, Changsha, China |
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| Abstract: | The low rank solution of the Q‐weighted nearest correlation matrix problem is studied in this paper. Based on the property of Q‐weighted norm and the Gramian representation, we first reformulate the Q‐weighted nearest correlation matrix problem as a minimization problem of the trace function with quadratic constraints and then prove that the solution of the minimization problem the trace function is the stationary point of the original problem if it is rank‐deficient. Finally, the nonmonotone spectral projected gradient method is constructed to solve them. Numerical examples illustrate that the new method is feasible and effective. Copyright © 2015 John Wiley & Sons, Ltd. |
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| Keywords: | nearest correlation matrix problem Q‐weighted norm low rank solution sufficient condition nonmonotone spectral projected gradient method |
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