Abstract
The calculus of concave functions is a widely accepted tool for optimum experimental design problems. However, as a function of the support points and the weights the design problem fails to be concave. In this paper we make use of generalized gradients in the sense of Rockafellar (1980) and Clarke (1983). A chain rule is presented for the subdifferential of the composition of an information function with the moment matrix mapping. Lipschitz continuity of the global design function is proved and conditions for strict differentiability are given.
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Wilhelm, A. Subdifferentiability and lipschitz continuity in experimental design problems. Metrika 42, 365–377 (1995). https://doi.org/10.1007/BF01894334
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DOI: https://doi.org/10.1007/BF01894334