Abstract
In this paper, we study multidisciplinary optimization problems where the objective functions and the vector-valued mathematical models are not necessarily differentiable in a classical sense. Moreover, we assume that the state equation consists of several submodels, that is, unit-process models. This study is based on the nonsmooth analysis introduced by Clarke and the theory of H-differentiable functions by Gowda. It concentrates on two mathematical tools needed in sensitivity analysis of the multidisciplinary optimization problems, namely, the generalized chain rule for vector-valued functions and the implicit subdifferentiation formula. We employ these tools to obtain subgradient information of the problems considered. Finally, we present a numerical example and compare the obtained results with finite differences by means of accuracy and computational efficiency.
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Madetoja, E., Mäkelä, M.M. On sensitivity analysis of nonsmooth multidisciplinary optimization problems in engineering process line applications. Struct Multidisc Optim 31, 355–362 (2006). https://doi.org/10.1007/s00158-005-0591-4
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DOI: https://doi.org/10.1007/s00158-005-0591-4