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I am reading a paper about optimsation and the description, while mostly being a very good description, makes reference to some variables being in some set $E$. For example, it states that parameter $x\in E^n$. However it does not mention the significance of $E$ or why it did not say $\mathbb{R}$ instead. I suppose the algorithm in discussion doesn't only apply to reals, but also complex numbers, etc. I am wondering though, whether the description merely means $E$ to mean, "some set," or if they mean something more specific. For example it could mean E to stand for "enumerated," which I guess would mean they only mean to refer to "computer-representable" numbers, which I guess technically is a subset of $\mathbb{R}$. I am not familiar with any special significance of the letter $E$ in engineering as applied to sets, so I wanted to make sure by asking.

Here is the description from the paper:

http://i.imgur.com/6doIW.png

Can anyone please give me their best interpretation of $E$ here? Thanks.

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    I do not think $E$ is a set. Probably $E^n$ is meant to stand for Euclidean $n$-space.2012-07-10

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$E^n$ is often used to denote $n$-dimensional Euclidean space, which is the same as $\mathbb R^n$. The symbol $E$ is often used to emphasize that the author is endowing $\mathbb R^n$ with the Euclidean inner product, or dot product, to make it into a Hilbert space. I've also seen it used to emphasize that $\mathbb R^n$ is being given a manifold structure.

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    Thanks! I didn't think of Euclidean for some reason. I usually see Euclidean space written $\mathbb{R}^n$, so it didn't occur to me! But your explanation makes perfect sense. In fact, in optimisation, distance is very important, so it would make sense that Euclidean properties should be defined.2012-07-10