Parameter estimation with (almost) deterministic global optimization

计算机辅助过程系统工程通过基于数学模型预测现实世界的过程来支持工业和医疗部门。这些模型需要参数估计，只有确定性的全局优化允许得出结论的模型的适用性。然而，相对较小的问题已经具有挑战性的现有通用的确定性求解器。因此，我们希望开发一个（n）（几乎）确定性的全局优化方法与大数据集。我们利用一个更简单的估计问题的基础上的一个子集的数据和完整的估计问题，以减少整体的计算负担之间的相似性。详细地说，我们建议使用简单的问题的下限内的分支定界方法来解决完整的问题。每当需要时，我们通过数据扩充步骤来调整简单问题的大小。由于单个数据点可能会影响全局解，因此我们提出的方法只能在一定的置信水平下才是确定性的。我们设想的参数估计更复杂的应用，从工业相关过程的反应动力学的传染病的传播。此外，我们的方法也可以应用于其他团体的软件工具。

Computer-aided process systems engineering supports the industrial and medical sector by predicting real-world processes based on mathematical models. These models require parameter estimation and only deterministic global optimization allows to conclude on the suitability of the model. However, comparatively small problems are already challenging for existing general-purpose deterministic solvers. Thus, we want to develop a(n) (almost) deterministic global optimization approach with large data sets. We exploit the similarities between a simpler estimation problem based on a subset of the data and the complete estimation problem to decrease the overall computational burden. In detail, we propose to use the simple problem for the lower bounding within the branch-and-bound method for solving the complete problem. Whenever required, we adapt the size of the simple problem by a data augmentation step. Since single data points may affect the global solution, our proposed approach can be deterministic only with respect to a certain confidence level. We envision the parameter estimation for more complex applications ranging from reaction kinetics of industry-relevant processes to the spread of an infectious disease. Besides, our methodology can be applied by software tools of other groups, too.