To avoid deviations outside the expected range of the parameters during the initial stages of the solution, linear interval inequality constraints of the form:
are enforced on the parameters. In the above equation L and U are
vectors of lower and upper bounds on each of the model parameters. The
constraints are incorporated into the Levenberg-Marquardt algorithm using
a simple technique based on the concept of active constraints [25].
A constraint becomes active if it is violated when the parameters are updated
(i.e. if 
or if 
). It remains active as long as the
negative gradient direction is pointing away from the feasible region. The
parameters corresponding to the set of active constraints are not allowed to
change by enforcing that 
. This is accomplished by
removing the appropriate equations from the linear system of
(2.26).