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Differentiability of Consistency Functions for DAE Systems

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Abstract

In the present paper, parametric initial-value problems for differential-algebraic (DAE) systems are investigated. It is known that the initial values of DAE systems must satisfy not only the original equations in the system but also the derivatives of these equations with respect to time. Whether or not this actually imposes additional constraints on the initial values depends on the particular problem.

Often the initial values are not determined uniquely, so that the resulting degrees of freedom can be used to optimize a given performance index. For this purpose, the class of so-called consistency functions is defined. These functions map a set of parameters, which include also those undetermined initial values, to consistent initial values for the DAE system.

Because of frequent gradient evaluations of the performance index and the constraints with respect to these system parameters needed by many optimization procedures, we state conditions such that the consistency functions represent differentiable functions with respect to these parameters.

Several examples are provided to illustrate the verification of the theoretical assumptions and their differentiability properties.

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Authors and Affiliations

  1. Assistant Professor, Department of Mathematics, University of Bayreuth, Bayreuth, Germany

    C. Büskens & M. Gerdts

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  1. C. Büskens
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  2. M. Gerdts
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The authors would like to thank the referees for helpful suggestions and comments

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Büskens, C., Gerdts, M. Differentiability of Consistency Functions for DAE Systems. J Optim Theory Appl 125, 37–61 (2005). https://doi.org/10.1007/s10957-004-1710-x

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