# Tagged Questions

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

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### Linear programming: Maximize minimum of linear functions

For a project I need something solved, it screams linear programming. If I get the problem in "standard" form I should be able to solve it using the simplex method. But I don't see how to get it in ...
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### Checking feasibility of a system of inequalities with scipy

I have a set of pairwise constraints, like this: a > b, b > c, c > a and need to check if they are satisfiable (in the example above, they are not). ...
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### Necessary condition for existence of a positive solution of a linear system

I would like to know what are the necessary conditions of existence of a positive (componentwise) solution of the system : Ax=b, with A a square ...
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### Binary integer variables in linear programming

Could someone please explain the concept of switch variables (binary integer decision variables) in linear programming? This example has two alternative constraints \begin{array}{ll} \text{...
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### Solve $\max_X \mathrm{sum}(AXB \geq \gamma)$, with $X$ being a permutation matrix

I have a problem to find the best permutation matrix $X \in \{0,1\}^{n \times n}$, which would maximizes the number of elements in $AXB$ which are above a certain positive number $\gamma$. In other ...
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### Find optimum diagonal matrix $D$ to maximize $ADB$ above a threshold $\gamma$

I have a problem to find the optimum diagonal matrix $D$, which would maximizes the number of elements in $ADB$ which are above a certain positive number $\gamma$. In other words, the problem is ...
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### Linear Programming formulate if then constraint

Consider an LP for which you want to add the restriction that Only if $x_1\geq 3$ then $x_2$ and $x_3$ are allowed to be larger than $0$; otherwise $x_2$ and $x_3$ are $0$. Demonstrate how to ...
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### Finding Dual of non-standart programming problem

I am working in optimization field. My programming problem is not of the standart form, however it is convex. Objective is nonlinear but concave (log of product). I do maximization. Constaints: ...
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### simplex method tableau

If I have the matrix: x1 x2 s1 s2 s3 z 1 4 1 0 0 0 | 12 2 5 0 1 0 0 | 2 1 3 0 0 0 1 | 4 ---------------- -2 -1 0 0 0 1 | 0 Then, where x1 is the row of 1, 2, 1....x2 is the row of 4, 5, 4.......
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