Name
Title | ||
|---|---|---|
A Quadratically Convergent Newton Method for Computing the Nearest Correlation Matrix |
Abstract | ||
|---|---|---|
The nearest correlation matrix problem is to find a correlation matrix which is closest to a given symmetric matrix in the Frobenius norm. The well-studied dual approach is to reformulate this problem as an unconstrained continuously differentiable convex optimization problem. Gradient methods and quasi-Newton methods such as BFGS have been used directly to obtain globally convergent methods. Since the objective function in the dual approach is not twice continuously differentiable, these methods converge at best linearly. In this paper, we investigate a Newton-type method for the nearest correlation matrix problem. Based on recent developments on strongly semismooth matrix valued functions, we prove the quadratic convergence of the proposed Newton method. Numerical experiments confirm the fast convergence and the high efficiency of the method. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1137/050624509 | SIAM J. Matrix Analysis Applications |
Keywords | Field | DocType |
methods converge,convergent method,quadratically convergent newton method,differentiable convex optimization problem,nearest correlation matrix,correlation matrix,newton-type method,nearest correlation matrix problem,gradient method,proposed newton method,symmetric matrix,semismooth matrix,objective function,convex optimization,newton method,quasi newton method,value function,quadratic convergence | Convergent matrix,Quasi-Newton method,Mathematical optimization,Jacobian matrix and determinant,Mathematical analysis,Matrix (mathematics),Matrix function,Symmetric matrix,Newton's method in optimization,Mathematics,Matrix splitting | Journal |
Volume | Issue | ISSN |
28 | 2 | 0895-4798 |
Citations | PageRank | References |
73 | 3.63 | 14 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Houduo Qi | 1 | 437 | 32.91 |
| Defeng Sun | 2 | 1475 | 91.95 |