T-optimal design for multivariate polynomial regression using semidefinite programming
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We consider T-optimal experiment design problems for discriminating multivariate polynomial regression models where the design space is defined by polynomial inequalities and the regression parameters are constrained to given convex sets. The original optimality criterion is reformulated as a convex optimization problem with a moment cone constraint. In the case of univariate regression models, an exact semidefinite representation of the moment cone constraint can be applied to obtain an equivalent semidefinite program. For general multivariate cases, we apply a moment relaxation technique and approximate the moment cone constraint by a hierarchy of semidefinite-representable outer approximations. When the relaxation hierarchy converges, the optimal discrimination design can be recovered from the optimal moment matrix, and its optimality confirmed by an equivalence theorem. The methodology is illustrated with several examples.
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