An adaptive discretization algorithm for locally optimal experimental design with constraints

TL;DR

This paper introduces an adaptive discretization algorithm for constrained experimental design that converges to an optimal or near-optimal solution with less computational effort and broader applicability.

Contribution

The paper presents a novel iterative adaptive discretization algorithm for constrained experimental design, improving efficiency and generality over existing methods.

Findings

Algorithm converges to optimal design when epsilon=0.

Finitely terminates at epsilon-optimal design for epsilon>0.

Demonstrates good convergence on chemical engineering problems.

Abstract

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 $\eps$-optimality condition for the current design. We prove that with $\eps = 0$, our algorithm converges to an optimal design and that with $\eps > 0$, our algorithm finitely terminates at an $\eps$-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.