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Does the input notation to this fitness function describe (represent) a Kleene star?

In an optimization problem; given an input space $X$ and a fitness function $f\;:\;X\mapsto\mathbb{R}$; the goal is to find the best $x^* \in X$ such that $f(x^*)=max_{x} f(x)$

If so would this $f(x^*)=max_{x} f(x)$ then read: The fitness function, given 0 to many values of $x \in X$ finds the maximum value of $x$?

William Elliot
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tkolleh
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    No, $x^*$ is an element of $X$, namely the one where $f$ attains its largest value. – Andreas Blass Oct 02 '20 at 21:10
  • @AndreasBlass How is your interpretation determined? What steps could I have taken to better understand the intent of the author of the function. Without having to find the author and ask.

    In-short, is that the common interpretation?

     – tkolleh Oct 02 '20 at 22:07
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    My "interpretation" is just restating what you already quoted: "$x^\in X$ such that $f(x^)=\max_xf(x)$. No special knowledge about the author or his intention is needed, just a reading of what he wrote. – Andreas Blass Oct 03 '20 at 16:15
  • @AndresBlass , Understood. Post/paste your answer and ill accept it. – tkolleh Oct 04 '20 at 03:32

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Using $x^*$ to denote a particular element of some larger set $X$ is a fairly common convention.

For it to be a Kleene star, you'd need a separate $x$ for it to be a Kleene star of. But in $f(x*)=\max_{x}f(x)$, $x$ is a bound/dummy variable, so there is no independent $x$ to take the Kleene star of. Therefore, the author can't have meant Kleene star.

tkolleh
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Mark S.
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