Abstract
In this chapter, we make the connection between concentration of measure and probability constrained optimization. It is the use of concentration inequality that makes the problem of probability constrained optimization mathematically tractable. Concentration inequalities are the enabling techniques that make possible probability constrained optimization.
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Notes
- 1.
We say that, X and Y are identically distributed, or similar, or that Y is a copy of X, if \(\mathbb{P}_{X}\left(A\right) = \mathbb{P}_{Y}\left(A\right),\) where \(\mathbb{P}_{X}\left(A\right) = \mathbb{P}_{X}\left(X \in A\right)\) is a probability measure. A random element X in a measurable vector space is called symmetric, if X and − X are identically distributed. If X is a symmetric random element, then its distribution is a symmetric measure.
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Qiu, R., Wicks, M. (2014). Probability Constrained Optimization. In: Cognitive Networked Sensing and Big Data. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-4544-9_11
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DOI: https://doi.org/10.1007/978-1-4614-4544-9_11
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