An adaptive discretization algorithm for locally optimal experimental design with constraints

We develop a novel iterative algorithm for locally optimal experimental design under constraints, like budget or performance constraints. It is an adaptive discretization algorithm. In every iteration, a discretized version of the constrained-design problem is solved and then the discretization is adaptively refined by adding an approximate violator of a suitable sufficient $\text{eps}$-optimality condition for the current design. We prove that with $\text{eps}=0$, our algorithm converges to an optimal design and that with $\text{eps}>0$, our algorithm finitely terminates at an $\text{eps}$-optimal design. Compared to the existing algorithms on constrained experimental design, our algorithm comes with considerably less computational effort because the nonlinear subproblems in our algorithm have a smaller dimension and have to be solved only approximately and only in selected iterations (typically the last few). Additionally, our algorithm covers a considerably larger class of constraints. We demonstrate the good convergence properties of the algorithm on experimental design problems from chemical engineering that feature time and yield constraints.