Questions tagged [fourier-motzkin]

Fourier–Motzkin elimination is an algorithm for eliminating variables from a system of linear inequalities.

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Solutions to system using Fourier-Motzkin Elimination

I am trying to find a solution to this system using Fourier-Motzkin Elimination, but I don't know how to finish this. Here is what I have so far. $x_1-x_2\leq 0,\quad x_1-x_3\leq 0,\quad -2x_1+2x_2+...
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why “$7y\leq 29$, y odd or $7y \leq 26$, y even”?

When reading an example in "Fourier-Motzkin elimination extension to integer programming problems-H.P.Williams" : "Suppose we wished lo eliminate x between the following two inequalities \begin{align*...
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Fourier Motzkin elimination with positive coefficients only

How can we use Fourier-Motzkin elimination on system of inequalities with positive coefficients preceding each variable $x_1$ to $x_2$. Obviously, in this case we will only have an upper bound as a ...
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Find Inverse Fourier Transform

Find the inverse Fourier Transform of $$ { F(\omega)=\frac{1}{2\pi(a+j\omega)^2} \ } $$ using the convolution theorem. Hint: the Fourier Transform of $e^{-at} u(t)=\frac{1}{\sqrt{2\pi}(a+j\omega)} ...
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Fourier Motzkin Elimination and totally unimodularity

Suppose $A\in \mathbb R^{m\times n}$ and $b\in \mathbb R^m$, and $A$ is totally unimodular (TUM). For the system $$Ax\leq b,$$ suppose I use Fourier-Motzkin elimination to eliminate first $k$ ...
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Feasible point of a system of linear inequalities

Let $P$ denote $(x,y,z)\in \mathbb R^3$, which satisfies the inequalities: $$-2x+y+z\leq 4$$ $$x \geq 1$$ $$y\geq2$$ $$ z \geq 3 $$ $$x-2y+z \leq 1$$ $$ 2x+2y-z \leq 5$$ How do I find an interior ...
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Linear program with two equality constraints

Compute the minimal value of $$x_1 + 2x_2 + 3x_3$$ when $x_1$, $x_2$, $x_3$ satisfy $$x_1 − 2x_2 + x_3 = 4$$ $$−x_1 + 3x_2 = 5$$ and $$x_1 \ge 0, \qquad x_2 \ge 0, \qquad ...
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Minimal set of inequalities

I have a set of $m$ linear inequalities in $R^n$, of the form $$ A x \leq b $$ These are automatically generated from the specification of my problem. Many of them could be removed because they are ...