Dynamic optimization with complementarity constraints: Smoothing for direct shooting. (4th August 2020) - Caspari, Adrian; Lüken, Lukas; Schäfer, Pascal; Vaupel, Yannic; Mhamdi, Adel; Biegler, Lorenz T.; Mitsos, Alexander
Highlights: Dynamic optimization problems with state-dependend complementarity constraints solved using direct shooting for the first time. Theoretical analysis for well-posedness of nonsmooth and smoothed DAE Approach scales as good as existing approaches with DAE size and scales not with control variable intervals. Approach applied for small and medium scale case studies. Abstract: We consider optimization of differential-algebraic equations (DAEs) with complementarity constraints (CCs) of algebraic state pairs. Formulating the CCs as smoothed nonlinear complementarity problem (NCP) functions leads to a smooth DAE, allowing for the solution in direct shooting. We provide sufficient conditions for well-posedness. Thus, we can prove that with the smoothing parameter going to zero, the solution of the optimization problem with smoothed DAE converges to the solution of the original optimization problem. Four case studies demonstrate the applicability and performance of our approach: (i) optimal loading of an overflow weir buffer tank, (ii) batch vaporization setpoint tracking, (iii) operation of a tank cascade, and (iv) optimal start-up of a rectification column. The numerical results suggest that the presented approach scales favorably: the computational time for solution of the tank cascade problem scales not worse than quadratically with the number of tanks and does not scale with the control grid.