An efficient sparse approach to sensitivity generation for large-scale dynamic optimization

In this work, an efficient approach is proposed for the combined step-wise state and sensitivity integration tailored to the orthogonal collocation in finite elements integration method. The presented algorithm can be adapted to any one step integration method where gradients are available from the solution of the discretized system. Moreover, it is completely based on sparse matrix calculus, which makes it especially suitable for large-scale equation systems with a relative small number of independent variables. The relative computational effort in comparison to a state integration is small with a linear increase w.r.t. the number of independent variables. The performance of the developed algorithm has been tested on two case studies: the parameter estimation of a stiff implicit differential equation system with parameters directly connected to the differential states, and the dynamic optimization of a stiff general DAE system.