Abstract
We investigate the possibility of extending some results of Pazman 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.
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