(698c) Optimal Experimental Designs Robust to Implementation Errors

Optimal experimental design, also known as model-based design of experiments, is often used to refine confidence regions of estimated parameters for system models or to discriminate between candidate models. Because models that are nonlinear in parameters yield designed experiments that depend on a priori parameter estimates, optimization problems have been formulated to yield designs that are robust to initial parameter uncertainty. Here we consider robustness in another sense. In general, a designed experiment is also subject to implementation errors: when a real-world experiment is implemented, the manipulated variables for the experiment will never be set precisely as the design indicates. We propose a max-min optimization formulation to give an informative experiment in the worst case of implementation errors in some uncertainty ?box? containing the origin. Robustness in this sense for optimal experimental design has never been reported before, however it has been recently reported for design of electromagnetic scattering devices and radiation therapy for cancer [1,2]. We demonstrate an example experimental system where this yields a more informative experiment, and overview an algorithm for solving the max-min optimization problem, by reformulating it as a semi-infinite program and using differential inequalities in conjunction with the interval-constrained reformulation of Bhattacharjee et al. (2005) [3].

References

[1] D. Bertsimas, O. Nohadani, and K. M. Teo, Robust optimization in electromagnetic scattering problems, Journal of Applied Physics, 101 (2007), pp. 1-7

[2] D. Bertsimas, O. Nohadani, and K. M. Teo, Nonconvex robust optimization for problems with constraints, INFORMS Journal on Computing, (2009), pp. 1-15

[3] B. Bhattacharjee, W.H. Green, P.I. Barton, Interval methods for semi-infinite programs, Computational Optimization and Applications, 30 (2005), pp. 63-93