Abstract
The future cannot be predicted exactly, but one may learn from past observations. Past decisions can also improve future predictability. This is the context in which decisions are generally made. Herein, we discuss some mathematical issues pertaining to this topic.
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Notes
- 1.
Throughout this book, without loss of generality, optimization problems are formulated as minimization problems, hence the objective function to be minimized is called a cost.
- 2.
The official web page of the SP community http://www.stoprog.org/ offers links to several tutorials and examples of applications of SP.
- 3.
Those quotes around the word state become clearer when discussing the Markovian case by the end of this subsection.
- 4.
What we call here “\(N\) samples or sample realizations” may be referred elsewhere in this book as a \(N\)-sample, whereas \(N\) is referred to as the number of samples or as the size of the \(N\)-sample.
- 5.
Later on in this book (see Sect. 6.1), we discuss the concept of Voronoi cells: here we are defining the \(N\) Voronoi cells of the segment \([-1,1]\) which are based on the “centroids” \(w_{0}^{i}\).
- 6.
Actually, in Fig. 1.5, a “forest”, that is, a collection of trees, rather than a “tree”, is depicted since there are several “root nodes” which are the nodes at the first level. But we keep on speaking of “trees” to match the traditional terminology of “scenario tree”.
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© 2015 Springer International Publishing Switzerland
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Carpentier, P., Chancelier, JP., Cohen, G., De Lara, M. (2015). Issues and Problems in Decision Making Under Uncertainty. In: Stochastic Multi-Stage Optimization. Probability Theory and Stochastic Modelling, vol 75. Springer, Cham. https://doi.org/10.1007/978-3-319-18138-7_1
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DOI: https://doi.org/10.1007/978-3-319-18138-7_1
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