Name
Title | ||
|---|---|---|
A Sequential Semismooth Newton Method for the Nearest Low-rank Correlation Matrix Problem |
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1137/090771181 | SIAM Journal on Optimization |
Keywords | Field | DocType |
sequential semismooth newton method,semidefinite programming problem,numerical method,nonconvex sdp,least-square problem,numerical result,nearest low-rank correlation matrix,large scale problem,sequential method,semismooth newton method,quadratic convergence | Mathematical optimization,Matrix (mathematics),Symmetric matrix,Stationary point,Rate of convergence,Numerical analysis,Semidefinite programming,Mathematics,Eigenvalues and eigenvectors,Newton's method | Journal |
Volume | Issue | ISSN |
21 | 4 | 1052-6234 |
Citations | PageRank | References |
16 | 0.67 | 15 |
Authors | ||
2 | ||