On sensitivity analysis of nonsmooth multidisciplinary optimization problems in engineering process line applications

Authors: Madetoja, Elina¹; Mäkelä, Marko²

Source: Structural and Multidisciplinary Optimization, Volume 31, Number 5, May 2006 , pp. 355-362(8)

Publisher: Springer

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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.

Keywords: Nonsmooth optimization; H-differentiability; Generalized chain rule; Implicit subdifferentiation formula

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s00158-005-0591-4

Affiliations: 1: Email: elina.madetoja@iki.fi 2: Email: marko.makela@mit.jyu.fi

Publication date: 2006-05-01