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What does "min" indicate infront of a sigma sign?

$$\min \sum_{e\in E} c_e x_e$$

Source: https://www.math.unipd.it/~luigi/courses/metmodoc1718/m08.01.TSPexact.en.pdf

Christoph
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Ryan Cameron
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  • We need more context, the way it's written makes no sense. Please explain what's $E$, $c_e$ and $x_e$ also is there anything below the minimum? Anyway the fact that $\min$ comes before the $\sum$ shouldn't make much difference it is still a minimum of numbers, I guess the numbers are somehow obtained by applying the $\sum$. – Yanko Dec 08 '18 at 22:40

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The $c_e$ are some constants, the $x_e$ are variables that satisfy some constraints and you are minimizing the sum $\sum_{e\in E} c_e x_e$ over all feasible choices of the $x_e$.

Christoph
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  • What does it mean to minimize the sum over all feasible choices? – Ryan Cameron Dec 08 '18 at 22:58
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    Each feasible choice (i.e. choice of the $x_e$ satisfying all constraints) gives you one value of the sum. You want to find the smallest value you can get. – Christoph Dec 08 '18 at 23:16