Numerical experiments with an inexact Jacobian trust-region algorithm

We present the adaptation and implementation of a composite-step trust region algorithm, developed in (Walther, SIAM J. Optim. 19(1):307-325, 2008), that incorporates the approximation of the Jacobian of the equality constraints with a specialized quasi-Newton method. The forming and/or factoring of the exact Jacobian in each optimization step is avoided. Hence, the presented approach is especially well suited for equality constrained optimization problems where the Jacobian of the constraints is dense. In this study, we discuss the calculation of the normal and tangential steps and how the trust region radius is adapted to take the inaccurate first-order information into account. Results are presented for several examples from the CUTE test set and a simple periodic adsorption process.