CLA--LASSO identity for singular covariance matrices

Determine whether the identity between the Markowitz Critical Line Algorithm path and the LASSO path remains valid when the covariance matrix is singular.

Background

The paper’s practical method relies on transforming the mean–variance optimization problem into a least-squares problem through a square root or factorization of the covariance matrix, and on the established correspondence between the Critical Line Algorithm and the LASSO path.

The stated scope excludes singular covariance matrices because the authors indicate that the identity has not been established in that setting. Extending or characterizing the correspondence for singular covariance matrices is therefore an explicitly unresolved question.