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# Questions tagged [linear-programming]

Questions on linear programming, the optimization of a linear function subject to linear constraints.

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### Difficult discrete optimization “knapsack” type problem [duplicate]

Take a bounded domain $S$ in which an explosive device is located. A team is deployed to find and disable the device before time $t^{*}$, when it will explode. There are certain constraints in place....
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### Both primal and dual have a unique optimal solution. Something wrong in the assumption/theorem/example?

The answer here mentioned a table from Sierksma's $\textit{Linear and Integer Programming: Theory and Practice}$, Volume 1, page 144. Both primal and dual are under standard form in table below (Here ...
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### How can I solve this linear optimization problem?

I've come across a question which I was not able to solve I would appreciate if someone could help me out here. Q) Given the constraints, $$x \ge 0$$ $$y \ge 0$$ $$x + y \le1$$ which of the ...
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### Upper bound of convergence of ellipsoid mathod

Actually, I am looking for a tighter upper bound for $(1+\frac{1}{n^2 - 1})^{n-1} (\frac{n}{n+1})^{2}$. It is easy to prove $(1+\frac{1}{n^2 - 1})^{n-1} (\frac{n}{n+1})^2 < e^{-\frac{1}{n+1}}$. ...
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### Does $A x > b$ have a solution?

Formulate a linear program that will determine whether or not $Ax>b$ has a solution, where $A$ is an $m \times n$ matrix and $b$ is an $m$-vector. We were told to use Farkas Lemma, but are not ...
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### Nested Linear Program [duplicate]

I have a linear program: minimise $f^T x$ with equality and inequality constraints. This does not have a unique solution, so I would like to find the solution of this that also minimises $g^T x$. ...
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### Rostering problem - variation of the post office problem

Suppose I have $N$ staff members. I employ each of them for 5 days during the week. Each day, $i$, from Saturday to Friday requires $s_i$ staff members. I wish to maximize the number of staff who ...
34 views