Abstract
E-optimal experimental designs for a second order response surface model with k 1 predictors are investigated. If the design space is the k-dimensional unit cube, Galil and Kiefer (1977a) determined optimal designs in a restricted class of designs (dened by the multiplicity of the minimal eigenvalue) and stated their universal optimality as a conjecture. In this paper we prove this claim and show that these designs are in fact E-optimal in the class of all approximate designs. Morever, if the design space is the unit ball, E-optimal designs have not been found so far and we also provide a complete solution to this optimal design problem. The main diculty in the construction of
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