The solution of nonconvex parameter estimation problems with deterministic global optimization methods is desirable but challenging, especially if large measurement datasets are considered. We propose to exploit the structure of this class of optimization problems to enable their solution with the spatial branch-and-bound algorithm. In detail, we start with a reduced dataset in the root node and progressively augment it, converging to the full dataset. We show for nonlinear programs (NLPs) that our algorithm converges to the global solution of the original problem considering the full dataset. The implementation of the algorithm extends our open-source solver MAiNGO. A numerical case study with a mixed-integer nonlinear program (MINLP) from chemical engineering and a dynamic optimization problem from biochemistry both using noise-free measurement data emphasizes the potential for savings of computational effort with our proposed approach.

中文翻译：

---

用于大规模参数估计的具有不断增长的数据集的分支定界算法

使用确定性全局优化方法解决非凸参数估计问题是可取的，但具有挑战性，特别是在考虑大型测量数据集时。我们建议利用此类优化问题的结构，以使用空间分支定界算法来解决它们。具体来说，我们从根节点中的缩减数据集开始，并逐步对其进行扩充，最终收敛到完整数据集。我们证明，对于非线性程序（NLP），考虑到完整数据集，我们的算法收敛到原始问题的全局解。该算法的实现扩展了我们的开源求解器 MAiNGO。化学工程的混合整数非线性程序（MINLP）和生物化学的动态优化问题都使用无噪声测量数据的数值案例研究强调了我们提出的方法节省计算量的潜力。