  The Ensemble Kalman Filter method can be used as an iterative particle
numerical scheme for state dynamics estimation and control--to--observable
identification problems. In applications it may be required to enforce the
solution to satisfy equality constraints on the control space. In this work we
deal with this problem from a constrained optimization point of view, deriving
corresponding optimality conditions. Continuous limits, in time and in the
number of particles, allows us to study properties of the method. We illustrate
the performance of the method by using test inverse problems from the
literature.
