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Linear programming is the study of optimizing a linear function over a set of linear inequalities. The Simplex Method, Ellipsoid Method and Interior Point Method are popular algorithms to solve linear programs.

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For Ax = b, x and b unknown vectors, how do I solve the x that maximizes min(b_i)?

Given a matrix $A$, each element $A_{i,j} \geq 0$, find the vector $\vec x$ that maximizes the minimum element in $\vec b$ ($\vec b = A \vec x$). Note that this is not a linear equation system as I d …
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