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The Extended Gauss-Newton Method for Nonconvex Loss Functions and its Application to Time-Optimal Model Predictive Control

We introduce the eXtended Gauss-Newton (XGN) method, which extends the Generalized Gauss-Newton (GGN) method to a class of nonconvex loss functions with a well-behaved global minimum. We show linear local convergence of the XGN method to a stationary point, as well as global convergence in case of a linear residual function and linear constraints. As one possible application, we illustrate how the considered class of nonconvex loss functions can be used to approximate time-optimal behaviour within a Model Predictive Control (MPC) framework.