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

ADE项目的目标是开发具有最优性准则（DAEO）的微分代数方程组的建模和新的数值方法。在第一个资助期，DAEO数值模拟的关键方法是用其相关的Karush-Kuhn-Tucker （KKT）最优性必要条件取代DAEO的嵌入式非线性程序。该方法将DAE方程转化为特殊的非光滑微分代数方程（DAE）系统。特别是AVT的任务。SVT部分是将非光滑DAE系统的仿真/灵敏度分析方法应用于DAE系统，STCE部分侧重于模型残差的高阶导数和McCormick松弛的自动生成。后者构成了现有后续申请可能涵盖的第二个筹资期的基础。在第一个资助期，开发了daeo的数值模拟和灵敏度分析方法。在第二个阶段，我们的目标是解决最优控制，参数估计或基于模型的实验设计问题。为了解决上层NLP，我们打算使用基于梯度的数值优化算法，如顺序二次规划（SQP）或内点法。如有需要，底层嵌入式NLP应求解到全局最优，如采用Branch & Bound方法。

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.