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The experimental design literature has produced a wide range of algorithms optimizing estimator variance for linear models where the design-space is finite or a convex polytope. But these methods have problems handling nonlinear constraints or constraints over multiple treatments. This paper presents Newton-type algorithms to compute exact optimal designs in models with continuous and/or discrete regressors, where the set of feasible treatments is defined by nonlinear constraints. We carry out numerical comparisons with other state-of-art methods to show the performance of this approach.