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We develop general theory for finding locally optimal designs in a class ofsingle-covariate models under any differentiable optimality criterion. Yang andStufken [Ann. Statist. 40 (2012) 1665-1681] and Dette and Schorning [Ann.Statist. 41 (2013) 1260-1267] gave complete class results for optimal designsunder such models. Based on their results, saturated optimal designs exist;however, how to find such designs has not been addressed. We develop tools tofind saturated optimal designs, and also prove their uniqueness under mildconditions.

Saturated locally optimal designs under differentiable optimality criteria