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We propose a new approach for identifying the support points of a locallyoptimal design when the model is a nonlinear model. In contrast to the commonlyused geometric approach, we use an approach based on algebraic tools.Considerations are restricted to models with two parameters, and the generalresults are applied to often used special cases, including logistic, probit,double exponential and double reciprocal models for binary data, a loglinearPoisson regression model for count data, and the Michaelis--Menten model. Theapproach, which is also of value for multi-stage experiments, works both withconstrained and unconstrained design regions and is relatively easy toimplement.

Support points of locally optimal designs for nonlinear models with two parameters