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.
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de Cursi, E.S., Holdorf Lopez, R. (2020). Uncertainty Quantification in Optimization. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_56
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DOI: https://doi.org/10.1007/978-3-030-21803-4_56
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