5834 2017 eng 1132 1161 5 32 article 0 -- -- -- We propose a composite step method, designed for equality constrained optimization with partial differential equations. Focus is laid on the construction of a globalization scheme, which is based on cubic regularization of the objective and an affine covariant damped Newton method for feasibility. We show finite termination of the inner loop and fast local convergence of the algorithm. We discuss preconditioning strategies for the iterative solution of the arising linear systems with projected conjugate gradient. Numerical results are shown for optimal control problems subject to a nonlinear heat equation and subject to nonlinear elastic equations arising from an implant design problem in craniofacial surgery. Optimization Methods and Software 10.1080/10556788.2016.1241783 yes urn:nbn:de:0297-zib-53954 Lars Lubkoll Martin Weiser Anton Schiela Martin Weiser Numerical Mathematics Computational Medicine Weiser, Martin ECMath-CH9 MATHEON-A17