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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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Linear programming with a convergent coefficient
The following linear programming problem
$x_n = \arg\min c_n'x \mbox{ subject to } Ax<b$
has a changing coefficient $c_n$. We have that $c_n\rightarrow c_*$. What happens to the solution $x_n$? Does …