局部最优实验设计的自适应离散化算法
Adaptive discretization algorithms for locally optimal experimental design
AI总结：
本文提出了非线性预测模型局部最优实验设计的自适应离散化算法，改进了现有算法，并证明了其收敛性与有限步终止性，最后通过化学工程中的两个应用示例验证了算法的实用性。
摘要：
我们开发了用于非线性预测模型局部最优实验设计的自适应离散化算法。借助这些算法，我们在多个方面改进并完善了相关的最先进算法。我们为所提出的算法建立了新颖的终止性、收敛性和收敛速率结果。特别地，我们在对设计准则非常一般的假设下证明了次线性收敛速率结果，最值得注意的是，在设计准则为强凸且设计空间有限这一额外假设下证明了线性收敛结果。此外，我们证明了在近似最优设计处的有限步终止性，包括对终止前迭代次数的上界估计。最后，我们通过化学工程中的两个应用示例（一个稳态模型和一个动态模型）说明了所提算法的实际应用。
英文摘要：
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish novel termination, convergence, and convergence rate results for the proposed algorithms. In particular, we prove a sublinear convergence rate result under very general assumptions on the design criterion and, most notably, a linear convergence result under the additional assumption that the design criterion is strongly convex and the design space is finite. Additionally, we prove the finite termination at approximately optimal designs, including upper bounds on the number of iterations until termination. And finally, we illustrate the practical use of the proposed algorithms by means of two application examples from chemical engineering: one with a stationary model and one with a dynamic model.
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