ON THE EQUIVALENCE OF CONSTRAINED AND COMPOUND OPTIMAL DESIGNS

Constrained and compound optimal designs represent two well-known methods for dealing with multiple objectives in optimal design as reflected by two functionals phi1 and phi2 on the space of information matrices. A constrained optimal design is constructed by optimizing phi2 subject to a constraint on phi1, and a compound design is found by optimizing a weighted average of the functionals phi = lambdaphi1 + (1 - lambda)phi2, 0 less-than-or-equal-to lambda less-than-or-equal-to 1. We Show that these two approaches to handling multiple objectives are equivalent.