  We consider T-optimal experiment design problems for discriminating
multi-factor polynomial regression models where the design space is defined by
polynomial inequalities and the regression parameters are constrained to given
convex sets. Our proposed optimality criterion is formulated as a convex
optimization problem with a moment cone constraint. When the regression models
have one factor, an exact semidefinite representation of the moment cone
constraint can be applied to obtain an equivalent semidefinite program. When
there are two or more factors in the models, 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, an optimal discrimination design can be recovered from the optimal
moment matrix, and its optimality is confirmed by an equivalence theorem. The
methodology is illustrated with several examples.
