Common principal components & related multivariate models
Common principal components & related multivariate models
On the sum of the largest eigenvalues of a symmetric matrix
SIAM Journal on Matrix Analysis and Applications
A nonsmooth version of Newton's method
Mathematical Programming: Series A and B
Mathematical Programming: Series A and B - Special issue: Festschrift in Honor of Philip Wolfe part II: studies in nonlinear programming
Sensitivity analysis of all eigenvalues of a symmetric matrix
Numerische Mathematik
Complementarity and nondegeneracy in semidefinite programming
Mathematical Programming: Series A and B
Semismooth Matrix-Valued Functions
Mathematics of Operations Research
A Dual Approach to Semidefinite Least-Squares Problems
SIAM Journal on Matrix Analysis and Applications
Least-Squares Covariance Matrix Adjustment
SIAM Journal on Matrix Analysis and Applications
A Quadratically Convergent Newton Method for Computing the Nearest Correlation Matrix
SIAM Journal on Matrix Analysis and Applications
An inexact primal–dual path following algorithm for convex quadratic SDP
Mathematical Programming: Series A and B
The rate of convergence of the augmented Lagrangian method for nonlinear semidefinite programming
Mathematical Programming: Series A and B
Calibrating Least Squares Semidefinite Programming with Equality and Inequality Constraints
SIAM Journal on Matrix Analysis and Applications
A Newton-CG Augmented Lagrangian Method for Semidefinite Programming
SIAM Journal on Optimization
Approximation of rank function and its application to the nearest low-rank correlation matrix
Journal of Global Optimization
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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.