# Tagged Questions

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

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### Analytic Center of Convex Polytope

I have a convex polytope defined by $Ax \leq b$. I want to know how to find the "analytic center" of my convex polytope, because my goal is to sample from the polytope using Monte-Carlo Markov ...
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### What kind of a problem is this?

The problem can be stated as: I have $m$ liquids ($A_i$ is the amount of the $i$-th liquid) and $n$ tanks ($x_j$ is the volume of the $j$-th tank), and the task is to find the best way to ...
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### Linear equations problem [closed]

The Marshall County trash incinerator in Norton burns 10 tons of trash per hour and co-generates 6 kilowatts of electricity, while the Wiseburg incinerator burns 5 tons per hour and co-generates 4 ...
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### How to Adequately Implement Phase I of Two-Phase Simplex Algorithm on a Computer with Floating Point Error

I'm currently trying to write some code that implements Phase I of the two-phase Simplex Algorithm described here: http://www.statslab.cam.ac.uk/~ff271/teaching/opt/notes/notes8.pdf In order to test ...
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### Tutorial for Simplex Method with No Slack Variables

I found a nice tutorial here http://www.math.ucla.edu/~tom/LP.pdf for applying the Simplex Method to problems of the form: maximize $c^T x$ with the constraints $Ax\leq b$, $x_i \geq 0$. It suggests ...
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### When is a quadratically constrained quadratic program (indefinite objective matrix) unbounded?

I have a nonconvex QCQP of the form $$x^TQ_0x + c^T x$$ such that $x^TQ_1x+c_1^Tx=b_1$, $Ax=b$, and $l\leq x\leq m$ where $Q_0$ is indefinite diagonal matrix and $Q_1$ is positive semidefinite ...
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### Using linear algebra (e.g. matrix) methods to solve a system of linear inequalities

Say we have the equation $Ax>b$, where $A$ is an M-by-N matrix, $b$ is a known vector of length N, x is an unknown vector of length N, and the inequality sign means that each element of $Ax$ is ...
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### What to do about equality constraints in the Simplex Tableau method

The question I've got is: Maximise $$2x-y+3z$$ subject to $$2y+z \leq 2$$ $$x+y+z=4$$ $$x-2y+z \geq 3$$ $$x,y,z \geq 0$$ Using the Simplex Tableau method. I know that for $\leq$ constraints you need ...
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### Minimize $w=9y_1+4y_2$ subject to linear inequalities

Minimize $w=9y_1+4y_2$ subject to : $4y_1+9y_2\geq 360$ $y_1+4y_2\geq 40$ $y_1\geq 0,~y_2\geq 0$