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.

翻译：本文针对非线性预测模型的局部最优实验设计问题，开发了自适应离散化算法。通过这些算法，我们在多个方面改进并完善了当前最先进的相关算法。我们为所提出的算法建立了新颖的终止性、收敛性及收敛速率结果。特别地，在设计准则满足非常一般的假设下，我们证明了算法具有次线性收敛速率；而更重要的是，在附加假设——设计准则强凸且设计空间有限——下，我们证明了算法具有线性收敛性。此外，我们证明了算法能在近似最优设计处有限步终止，并给出了终止所需迭代次数的上界。最后，我们通过化学工程中的两个应用实例——一个使用稳态模型，另一个使用动态模型——说明了所提出算法的实际应用价值。