Constrained Optimal Experimental Design: Theory, Algorithm and Applications

While the literature on optimal experimental design (OED) is primarily concerned with unconstrained problems, it is also of interest to restrict individual experiments, certain design quantities, or even the entire experimental plan. A classic approach to OED models the problem as an unconstrained optimization problem over the infinite dimensional space of probability measures.

This thesis introduces a general framework for constrained OED problems and discusses optimality criteria in form of saddle point conditions. Particular attention is paid to the required constraint qualifications. For the numerical solution of such constrained infinite-dimensional nonlinear OED problems this thesis proposes an adaptive discretization scheme, utilizing the derivative of the Lagrangian function. Furthermore, this thesis discusses the multi-criteria OED problem and presents algorithmic schemes for convex and non-convex objective functions. Finally, the algorithms are illustrated on an application example from chemical process engineering.