Globalization of Pantoja's optimal control algorithm

© 2002 Springer Science+Business Media New York. This is the accepted manuscript version of an article which has been published in final form at https://doi.org/10.1007/978-1-4613-0075-5_13In 1983 Pantoja described a stagewise construction of the Newton direction for a general class of discrete time optimal control problems. His algorithm incurs amazingly low overheads: the cost (measured in target function evaluations) is independent of the number of discrete time-steps. The algorithm can be modified to verify that the Hessian contains no eigen values less than a postulated quantity, and to produce an appropriate descent direction in the case where the Hessian fails to be positive definite and global convergence becomes an issue. Coleman and Liao have proposed a specific damping strategy in this context. Here we describe how Automatic Differentiation can be used to implement Pantoja’s algorithm, and we briefly consider some alternative globalization strategies, within which AD techniques can be further deployed.Final Accepted Versio