Nearest positive semi-definite covariance matrix

Find nearest positive semi-definite matrix to a symmetric matrix that is not positive semi-definite

The function performs a nonlinear, constrained optimization to find a positive semi-definite matrix that is closest (2-norm) to a symmetric matrix that is not positive semi-definite which the user provides to the function. The optimization is subject to the constraint that the output matrix' diagonal elements as well as its eigenvalues are non-negative.