I'm running a linear program whose parametrization depends on the output of a neural network. I was wondering if there exist results on how robust linear programs are towards perturbations in their parametrizations (i.e. if I add $\epsilon$ to the parametrization, how does that affect the solution). If there is no work on this: Do you have some (handwavy) intuition/argument on whether they should be "robust" or not?
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$\begingroup$ Search phrase: "sensitivity analysis" $\endgroup$– RobPrattCommented Apr 7, 2022 at 17:23
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$\begingroup$ The solution to a linear program is generically at an extreme point of the convex region defined by the constraints (which is an intersection of a finite number of half-planes). A small change in the parameters can take you to another extreme point, which can be quite far away. $\endgroup$– Aaron BergmanCommented Apr 7, 2022 at 23:43
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