Optimal design of experiments via linear programming.

We investigate the possibility of extending some results of Pázman and Pronzato (Ann Stat 42(4):1426-1451, 2014) to a larger set of optimality criteria. Namely, the problems of computing D-, A-, and $$E_k$$ -optimal designs in a linear regression model are reformulated here as 'infinite-dimensional' linear programming problems. The same approach is applied to combination of these optimality criteria and to the 'criterion robust' problem of Harman (Metrika 60:137-153, 2004). Approximate optimum designs can then be computed by a relaxation method (Shimizu and Aiyoshi in IEEE Trans Autom Control 25(1):62-66, 1980), and this is illustrated on various examples. [ABSTRACT FROM AUTHOR]