摘要
Based on the well-known result that the sum of the largest eigenvalues of a symmetric matrix can be represented as a semidefinite programming problem (SDP), we formulate the nearest low-rank correlation matrix problem as a nonconvex SDP and propose a numerical method that solves a sequence of least-square problems. Each of the least-square problems can be solved by a specifically designed semismooth Newton method, which is shown to be quadratically convergent. The sequential method is guaranteed to produce a stationary point of the nonconvex SDP. Our numerical results demonstrate the high efficiency of the proposed method on large scale problems.
源语言 | 英语 |
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页(从-至) | 1641-1666 |
页数 | 26 |
期刊 | SIAM Journal on Optimization |
卷 | 21 |
期 | 4 |
DOI | |
出版状态 | 已出版 - 2011 |
已对外发布 | 是 |