Beschreibung:
Constrained and compound optimal designs represent two well-known methods for dealing with multiple objectives in optimal design as reflected by two functionals φ<sub>1</sub> and φ<sub>2</sub> on the space of information matrices. A constrained optimal design is constructed by optimizing φ<sub>2</sub> subject to a constraint on φ<sub>1</sub>, and a compound design is found by optimizing a weighted average of the functionals φ = λφ<sub>1</sub> + (1 - λ)φ<sub>2</sub>, 0 ≤ λ ≤ 1. We show that these two approaches to handling multiple objectives are equivalent.