Schematic visualization of the eigenspectrum and proxy matrix approaches with respect to the cone of psd matrices. The cone interior covers the full-rank psd matrices, and the cone boundary contains the psd matrices having at least one zero eigenvalue. In the origin, we have the matrix with all eigenvalues zero. Out of the cone are the non-psd matrices. Both strategies project the matrices to the cone of psd-matrices. The parameter controls how strong the matrices are regularized toward a clipping solution with a matrix update A. Depending on the penalizer and the rank of S, the matrices follow various trajectories (an exemplary one is shown by the curved line in the cone). If ⁠, the path reaches the clipping solution at the boundary of the cone.