Model based optimal experimental design - a semidefinite programming approach applied to a solvent design problem

This paper introduces a mathematical programming approach to systematically find optimal designs of experiments for linear algebraic models. The method assumes that we have a fully specified parametric model with unknown parameters and the design criterion is convex. To address the problem we use a semi-definite programming formulation, originally developed by Vandenberghe and Boyd (1999), and propose a new global optimization based framework to determine D-optimal designs. The approaches are applied to an empirical response surface model to design an experimental design, and the mixture components are the composition of the solvent.