Aachen Dynamic Optimization Environment (ADE): Modeling and numerical methods for higher-order sensitivity analysis of differential-algebraic equation systems with optimization criteria

• Applicants: Professor Alexander Mitsos, Ph.D.; Professor Dr. Uwe Naumann
• Subject Area: Computer Architecture, Embedded and Massively Parallel Systems ; Software Engineering and Programming Languages
• Term: from 2016 to 2024
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 281932795

The objective of the ADE project is to develop modeling and novel numerical methods for differential-algebraic equations systems with optimality criteria (DAEO). In the first funding period, the key methodology for the numerical simulation of DAEOs was the substitution of the embedded nonlinear program of the DAEO by its associated Karush-Kuhn-Tucker (KKT) necessary conditions of optimality. This approach transforms DAEOs into special nonsmooth differential-algebraic equation (DAE) systems. In particular, the task of AVT.SVT part was to adapt methods for simulation/sensitivity analysis of nonsmooth DAE systems for DAEOs, while the STCE part focused on the automatic generation of higher-order derivatives and McCormick relaxations of the model residuals. The latter form the basis for a potential second funding period covered by the follow-up application at hand.In the first funding period, numerical methods for the simulation and sensitivity analysis of DAEOs were developed. In the second period we aim to solve optimal control, parameter estimation or model-based experimental design problems. To solve the upper level NLP, we intent to use gradient-based numerical optimization algorithms such as sequential quadratic programming (SQP) or interior point methods. If required, the lower level embedded NLP shall be solved to global optimality, e. g. by means of Branch & Bound methods.

• DFG Programme: Research Grants