  Recently, the school of Takemura and Takayama have developed a quite
interesting minimization method called holonomic gradient descent method (HGD).
It works by a mixed use of Pfaffian differential equation satisfied by an
objective holonomic function and an iterative optimization method. They
successfully applied the method to several maximum likelihood estimation (MLE)
problems, which have been intractable in the past. On the other hand, in
statistical models, it is not rare that parameters are constrained and
therefore the MLE with constraints has been surely one of fundamental topics in
statistics. In this paper we develop HGD with constraints for MLE .
