(119a) A Branch-and-Bound Algorithm with Growing Datasets for Large-Scale Parameter Estimation

Accurate results of parameter estimation problems are the basis for model-based optimization of process design and control. Only deterministic global optimization can ensure that suboptimal solutions are excluded as a reason for model-data mismatch [1,2]. However, general nonconvex parameter estimation problems considering large measurement datasets are challenging for state-of-the-art solvers. Thus, we propose to extend a common optimization method, the spatial branch-and-bound (B&B) algorithm [3,4], by using growing datasets. In detail, we propose to start with a reduced dataset in the root node of the B&B tree and augment it successively until converging to the original full dataset. We present different rules determining for each B&B node whether to augment the dataset or branch the parameter domain. By extending a proof of Locatelli and Schoen [5], we can show for nonlinear programs (NLPs) that our extension retains the convergence of the B&B algorithm. We implement the proposed extension in our open-source solver MAiNGO [6] and test the algorithm for a real-world case study stemming from chemical engineering, namely fitting an equation of state of propane [7]. The numerical results for this case study show significant CPU time savings.

Acknowledgement

This work was partially funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under grant MI 1851/10-1 “Parameter estimation with (almost) deterministic global optimization”.

Susanne Sass is grateful for her association to the International Research Training Group (DFG) IRTG-2379 Modern Inverse Problems under grant 333849990/GRK2379.

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References

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