Let the unpreturb problem be:
\begin{align} \min_{x}\quad & f_{0}\left(x\right) \\ \textrm{s.t.} \quad & f_{i}\left(x\right) \leq 0, i = 1 \dots m \\ & h_{i}\left(x\right) = 0, i = 1 \dots p \end{align}
Preturbed on is just:
\begin{align} \min_{x}\quad & f_{0}\left(x\right) \\ \textrm{s.t.} \quad & f_{i}\left(x\right) \leq u_{i} \\ & h_{i}\left(x\right) = v_{i} \end{align}
Global Tightness So we can get a lower bound:
\begin{equation} p^{*}\left(u,v\right) \geq g\left(\lambda^{*}, v^{*}\right) - u^{T} \lambda^{*} - v^{T}\lambda^{*} \end{equation}
by subtracting the original strictly feasible. if \lambda_{i} is large, if u decreases (i.e. u < 0), then p increases greatly if \lambda_{i} is small, if u increases (i.e. u >0), then we can’t say anything about p Local Sensitivity \begin{equation} \lambda_{i}^{} = - \pdv{p^{}\left(0,0\right)}{u_{i}} \end{equation}
\begin{equation} v_{i}^{*} = - \pdv{p^{*}\left(0,0\right)}{v_{i}} \end{equation}