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I have a MILP (Xpress) constraint, which is doing what I want it to, but I'm struggling to translate it into a LaTeX friendly mathematical expression.

The below code enforces that in the matrix $V$, the sum of the row indexed at seat, is less than or equal to the element in vector seat_vars, indexed at seat. In plain English, one or zero viewers can be assigned to each seat; put another may, at most one person could be assigned to each seat.

for seat in seat_vars.keys():
    constraint = [V[seat, v] for v in range(1, num_viewers+1)]
    sum_ = solver.Sum(constraint)
    solver.Add(sum_ <= seat_vars[seat])

What is the proper mathematical way to express this in LaTeX?

The best I've got so far is

$$ \sum_{i=1}^{n} V_{\text{seat},i} \leq \text{seatvars}_{\text{seat}} $$

However, I'm unsure how to "for loop" over every seat; eg this constraint holds for each seat.

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1 Answer 1

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Okay...
$\sum_{i=1}^n V_{seat,i} \le seatvars_{seat} \quad \forall seat \in\ $seatVars
Looping 'for' in done by $\forall$

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