Given a symmetric matrix

$G$, one has to find a correlation matrix

$X$ (i.e., a positive semidefinite and symmetric matrix with diagonal elements equal to 1) which is closest to

$G$ in Frobenius norm. The dual of this constrained optimization problem is an unconstrained problem with an objective function that is not continuously differentiable. Hence a direct approach would result in at most linear convergence. However, its solution is obtained by solving a system of nonlinear equations involving the Frobenius norm of a projection onto the cone of positive semidefinite symmetric matrices. Since this projection is strongly semismooth, the authors succeed in designing a (nonsmooth) Newton method which they prove to be quadratically convergent which is confirmed by numerical experiments. Extensions are discussed which include minimizing a weighted Frobenius norm, imposing a lower bound on

$X$, and allowing

$X$ to be nonsymmetric.