We present an improvement of existing methods for globally solving optimal experimental design (OED) for bounded-error estimation based on a bilevel formulation from Mukkala et al. (2017). The proposed solution method for the min–max program is based on our method for generalized semi-infinite programs (via restriction of the right-hand side). The algorithm employed has the advantage that it guarantees a global solution for the OED assuming the global solution of two subproblems. To obtain a feasible solution only the lower-level problem has to be solved globally. In case of a local solution of the upper-level problem, the solution is still feasible though it is an upper bound of the global solution. The min–max method for OED is illustrated with four examples: two simple chemical reactions, BET-adsorption and a reformulated predator-prey system. The benefits of global methods are shown along with the limitations of state-of-the-art global solvers.

我们提出了一种对现有方法的改进，该方法基于Mukkala等人的双层公式，针对有界误差估计的全局求解最佳实验设计（OED）进行了整体求解。（2017）。min-max程序的拟议解决方法基于我们的广义半无限程序的方法（通过右侧的限制）。所采用的算法的优点在于，它假设两个子问题的全局解，就可以保证OED的全局解。为了获得可行的解决方案，只需要全局解决较低级别的问题。对于上级问题的本地解决方案，尽管它是全局解决方案的上限，但该解决方案仍然可行。OED的最小-最大方法用四个示例说明：两个简单的化学反应，BET吸附和重新配制的捕食者-猎物系统。