title: Model-based optimal design of experiments - semidefinite and nonlinear programming formulations.
abstract: We use mathematical programming tools, such as Semidefinite Programming (SDP) and Nonlinear Programming (NLP)-based formulations to find optimal designs for models used in chemistry and chemical engineering. In particular, we employ local design-based setups in linear models and a Bayesian setup in nonlinear models to find optimal designs. In the latter case, Gaussian Quadrature Formulas (GQFs) are used to evaluate the optimality criterion averaged over the prior distribution for the model parameters. Mathematical programming techniques are then applied to solve the optimization problems. Because such methods require the design space be discretized, we also evaluate the impact of the discretization scheme on the generated design. We demonstrate the techniques for findingD-,A- andE-optimal designs using design problems in biochemical engineering and show the method can also be directly applied to tackle additional issues, such as heteroscedasticity in the model. Our results show that the NLP formulation produces highly efficientD-optimal designs but is computationally less efficient than that required for the SDP formulation. The efficiencies of the generated designs from the two methods are generally very close and so we recommend the SDP formulation in practice.
authors.affiliation: Centro de Investigação em Processos Químicos e Produtos da Floresta, Department of Chemical Engineering, University of Coimbra, Pólo II, R. Sílvio Lima, 3030-790 Coimbra, Portugal. Tel. +351 239 798700; Department of Chemical and Biological Engineering, ISEC, Polytechnic Institute of Coimbra, R. Pedro Nunes, 3030-199 Coimbra, Portugal. Tel. +351 239 790200.
authors.forename: Belmiro P M
authors.initials: BP
authors.lastname: Duarte
authors.affiliation: Department of Biostatistics, Fielding School of Public Health, UCLA, 10833 Le Conte Ave., Los Angeles, California 90095-1772, U.S.A.
authors.forename: Weng Kee
authors.initials: WK
authors.lastname: Wong
authors.affiliation: Centro de Investigação em Processos Químicos e Produtos da Floresta, Department of Chemical Engineering, University of Coimbra, Pólo II, R. Sílvio Lima, 3030-790 Coimbra, Portugal. Tel. +351 239 798700.
authors.forename: Nuno M C
authors.initials: NM
authors.lastname: Oliveira
keywords: Approximate Design; Bayesian Optimal Design; Gaussian Quadrature Formula; Global Optimization; Information Matrix