Optimal design of experiments via linear programming

TL;DR

This paper extends results on optimal experimental design by formulating various optimality criteria as infinite-dimensional linear programming problems and proposes a modified cutting-plane method for computing approximate solutions.

Contribution

It generalizes optimal design criteria to a broader set and introduces a linear programming approach with a modified cutting-plane method for practical computation.

Findings

Successfully reformulated optimality criteria as linear programming problems

Developed a modified cutting-plane algorithm for approximate design computation

Validated the approach on example problems

Abstract

We investigate the possibility of extending some results of Pazman and Pronzato (2014) to a larger set of optimality criteria. Namely, in a linear regression model the problem of computing D-, A-, E_k-optimal designs, of combining these optimality criteria, and the "criterion robust" problem of Harman (2004) are reformulated here as "infinite-dimensional" linear programming problems. Approximate optimum designs can then be computed by a modified cutting-plane method, and this is checked on examples. Finally, the expressions for these criteria are reformulated in terms of the response function of an even nonlinear model.