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Dynamic Optimization with Complementarity Constraints: Smoothing for Direct Shooting

Adrian Caspari (adrian.caspari***at***avt.rwth-aachen.de)
Lukas Lüken (lukas.lueken***at***rwth-aachen.de)
Pascal Schäfer (pascal.schaefer***at***avt.rwth-aachen.de)
Yannic Vaupel (yannic.vaupel***at***avt.rwth-aachen.de)
Adel Mhamdi (adel.mhamdi***at***avt.rwth-aachen.de)
Lorenz T. Biegler (biegler***at***cmu.edu)
Alexander Mitsos (amitsos***at***alum.mit.edu)

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.

Keywords: MPCCs with DAE, direct single-shooting, well-posedness analysis, optimization of regularized nonsmooth DAE

Category 1: Nonlinear Optimization

Category 2: Nonlinear Optimization (Systems governed by Differential Equations Optimization )

Category 3: Complementarity and Variational Inequalities

Citation: Adrian Caspari, Lukas Lüken, Pascal Schäfer, Yannic Vaupel, Adel Mhamdi, Lorenz T. Biegler, Alexander Mitsos. Dynamic Optimization with ComplementarityConstraints: Smoothing for Direct Shooting. Computers and Chemical Engineering. 2020. doi: https://doi.org/10.1016/j.compchemeng.2020.106891

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Entry Submitted: 10/01/2019
Entry Accepted: 10/01/2019
Entry Last Modified: 05/26/2020

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