Optimal design of experiments via linear programming

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.