Name
Title | ||
|---|---|---|
Newton's Method for Computing the Nearest Correlation Matrix with a Simple Upper Bound. |
Abstract | ||
|---|---|---|
The standard nearest correlation matrix can be efficiently computed by exploiting a recent development of Newton’s method
(Qi and Sun in SIAM J. Matrix Anal. Appl. 28:360–385, 2006). Two key mathematical properties, that ensure the efficiency of the method, are the strong semismoothness of the projection
operator onto the positive semidefinite cone and constraint nondegeneracy at every feasible point. In the case where a simple
upper bound is enforced in the nearest correlation matrix in order to improve its condition number, it is shown, among other
things, that constraint nondegeneracy does not always hold, meaning Newton’s method may lose its quadratic convergence. Despite
this, the numerical results show that Newton’s method is still extremely efficient even for large scale problems. Through
regularization, the developed method is applied to semidefinite programming problems with simple bounds. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/s10957-010-9738-6 | J. Optimization Theory and Applications |
Keywords | Field | DocType |
correlation matrix,projection operator,condition number,upper bound,quadratic convergence | Mathematical optimization,Condition number,Matrix (mathematics),Upper and lower bounds,Positive-definite matrix,Projection (linear algebra),Rate of convergence,Semidefinite programming,Mathematics,Newton's method | Journal |
Volume | Issue | ISSN |
147 | 3 | 15732878 |
Citations | PageRank | References |
1 | 0.36 | 19 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Qingna Li | 1 | 19 | 2.41 |
| Donghui Li | 2 | 380 | 32.40 |
| Houduo Qi | 3 | 437 | 32.91 |