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 φ1 and φ2 on the space of information matrices. A constrained optimal design is constructed by optimizing φ2 subject to a constraint on φ1, and a compound design is found by optimizing a weighted average of the functionals φ = λφ1 + (1 - λ) φ2, 0 ≤ λ ≤ 1. We show that these two approaches to handling multiple objectives are equivalent.