Perturbation function
= Perturbation function
{title2=$f(x,u)$}
A <perturbation function> encodes a family of objectives and constraints indexed by a perturbation $u$, with the original problem at $u=0$. Extended-real values encode constraints. Its marginal $p(u)=\inf_xf(x,u)$ measures the optimal value's response to perturbation; jointly convex data give <convex perturbation duality>.