  Model reduction methods often aim at an identification of slow invariant
manifolds in the state space of dynamical systems modeled by ordinary
differential equations. We present a predictor corrector method for a fast
solution of an optimization problem the solution of which is supposed to
approximate points on slow invariant manifolds. The corrector method is either
an interior point method or a generalized Gauss--Newton method. The predictor
is an Euler prediction based on the parameter sensitivities of the optimization
problem. The benefit of a step size strategy in the predictor corrector scheme
is shown for an example.
