Consider the linear program $f(c)=\min\{c'x\mid x\in\mathbb{R}^n,Ax=b,x\geq0\}$. Are there any results on what is $\partial f/\partial b$?
2026-04-23 15:47:20.1776959240
Subgradient of the optimal value of a linear program with respect to its parameters
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This is answered by the sensitivity interpretation of the Lagrange multipliers. (Linear programming books or convex optimization books should discuss the sensitivity interpretation.) If $\lambda$ is a Lagrange multiplier for the constraint $Ax = b$, then $-\lambda$ is a subgradient of $f$ at $b$.