FAST COMPUTATION OF THE HESSIAN OF THE LAGRANGIAN IN SHOOTING ALGORITHMS FOR DYNAMIC OPTIMIZATION

One approach to solve optimal control problems by direct methods is the so called sequential approach or single shooting. Only the control variables are discretized resulting in a NLP which can be solved with SQP or interior point methods. This paper presents a new methodology to efficiently provide the Hessian of the Lagrangian of that resulting NLP. The algorithm is based on the second- order adjoint method and introduces the novel concept of composite adjoints to reduce the computational effort of a Hessian evaluation. Though, this contribution is for sake of simplicity restricting to single shooting, the same methodology can also be easily applied to multiple shooting.