See this thread: http://forum.kde.org/viewtopic.php?f=74&t=106962
AMD introduces zeros at the beginning of the diagonal which is pretty bad. Ideally, SimplicialLDLT could even do numerical pivoting, either dynamically (difficult) or statically.
This changeset https://bitbucket.org/eigen/eigen/commits/ce076b6d66ce "push and keep structural empty diagonal elements to the bottom-right part of the matrix", meaning that SimplicialLDLT succeed at solving LS problems with linearly independent equality constraints enforced using the Lagrange multipliers method. This should be enough for 3.3.
I've backported it to 3.2: https://bitbucket.org/eigen/eigen/commits/e4cb52c98ae8/