In this dissertation, hierarchical optimization is applied in optimal experimental design for guaranteed parameter estimation, and the applicability and accessibility of hierarchical optimization methods are improved. Furthermore, we analyze the advantages and disadvantages of using global optimization in Bayesian optimization. Bayesian optimization using Gaussian processes as a surrogate model has been effectively used to optimize expensive to evaluate black-box-functions. In this context, we investigate the advantages and disadvantages of using deterministic global optimization for optimizing the acquisition function, by comparing the Bayesian optimization performance when using a deterministic global solver with two conventional solvers across four different test functions. In contrast to Bayesian optimization, optimal experimental design for guaranteed parameter estimation requires knowledge of the underlying model as an equation system. These models usually include parameters that must be estimated, and naturally, the parameter values are inherently uncertain. We extend the formulation of optimal experimental design for guaranteed parameter estimation to systems whose input-output relation is implicitly defined through an optimization problem, which corresponds in our application to the rigorous computation of liquid-liquid equilibria. The resulting optimization problem of the latter approach is a hierarchical program that is generally challenging to solve. Although multiple adaptive discretization-based methods for their solution have been proposed in recent decades, their numerical comparison is lacking. We remedy this by presenting an open-source software for solving multiple hierarchical optimization programs. Our software includes an extensive library of test problems, which we compiled from existing benchmark libraries and other problems in the literature. Utilizing our software and library of test problems, we compare multiple adaptive discretization-based solvers and conduct parameter tuning for the algorithmic parameters associated with each solver. On this basis, we propose an adaptation of an existing adaptive discretization-based method for solving bilevel programs, implement it in our software, and compare it to existing solvers, including the original approach. For the above-mentioned extended formulation for optimal experimental design for guaranteed parameter estimation, we present a specialized solution algorithm and provide a proof-of-concept, demonstrating the feasibility of our method. In many applications, including optimal experimental design for guaranteed parameter estimation, the necessary assumptions of the employed hierarchical optimization solvers may be violated. Therefore, we examine the necessary assumptions of an existing semi-infinite optimization method, and show that slightly weaker assumptions are possible. As many adaptive discretization-based solution algorithms have the examined solution algorithm as their predecessor, it can be presumed that the convergence guarantees shown with the more precise, slightly weaker assumptions are directly transferable from one algorithm to the other.
Daniel Jungen (Wed,) studied this question.