"Memory-efficient Newton/Pantoja method for optimal control problems"
Julia Sternberg University of Hamburg, Department of Mathematics
Abstract We investigate a memory-efficient Newton/Pantoja method for the nu-merical solution of optimal control problems. Using a local minimum principle we derive the first order necessary optimality conditions, that are equivalent to a nonlinear equation in appropriate Banach spaces. This equation issolved by a combination between the Newton and Pantoja methods. Each iteration of the Newton method, i.e. each application of the Pantoja method toevaluate a search direction, contains three alternative sweeps through a timehorizon, with a specific information dependence between different sweeps, sothat the straightforward implementation of the algorithm would require ahuge amount of memory to store all intermediate variables. To reduce thismemory requirement we develop nested checkpointing techniques and provesome theoretical results concerning them. Finally, we discuss numerical ex-periences considering an optimal control problem for laser surface hardeningof steel.
Two OPTEC professors have been awarded three "Gouden Krijtjes", the yearly teaching awards given by the organization of engineering students (vtk). Prof. Lombaert was awarded the prize for the best course in civil engineering, and Prof. Diehl the prizes for the best professor and the best course in mathematical engineering (where he teaches numerical optimization). They received these awards at the yearly "proffentap" where experienced students taught them how to draft beer professionally.
