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Uncertainty Quantification in Optimization

  • Eduardo Souza de Cursi
  • Rafael Holdorf LopezEmail author
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 991)

Abstract

We consider constrained optimization problems affected by uncertainty, where the objective function or the restrictions involve random variables \( \varvec{u} \). In this situation, the solution of the optimization problem is a random variable \( \varvec{x}\left( \varvec{u} \right) \): we are interested in the determination of its distribution of probability. By using Uncertainty Quantification approaches, we may find an expansion of \( \varvec{x}\left( \varvec{u} \right) \) in terms of a Hilbert basis \( {\mathcal{F}} = \left\{ {\varphi_{i} :i \in {\mathbb{N}}^{*} } \right\} \). We present some methods for the determination of the coefficients of the expansion.

Keywords

Optimization under uncertainty Uncertainty quantification Constrained optimization 

References

  1. 1.
    Lopez, R.H., De Cursi, E.S., Lemosse, D.: Approximating the probability density function of the optimal point of an optimization problem. Eng. Optim. 43(3), 281–303 (2011)  https://doi.org/10.1080/0305215x.2010.489607MathSciNetCrossRefGoogle Scholar
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    Lopez, R.H., Miguel, L.F.F., De Cursi, E.S.: Uncertainty quantification for algebraic systems of equations. Comput. Struct. 128, 189–202 (2013)  https://doi.org/10.1016/j.compstruc.2013.06.016CrossRefGoogle Scholar
  3. 3.
    De Cursi, E.S., Sampaio, R.: Uncertainty quantification and stochastic modelling with matlab. ISTE Press, London, UK (2015)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.LMNINSA Rouen Normandie, Normandie UniversitéSt-Etienne du RouvrayFrance
  2. 2.UFSCFlorianopolis SCBrazil

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