= Convex perturbation function
{title2=$f(x,z)$}
A jointly proper <convex function> $f(x,z)$ represents an optimization problem at perturbation $z=0$ and a family of nearby problems at other $z$. Its primal value function is $p(z)=\inf_x f(x,z)$. Relaxing an inequality by $z$ gives the example $f(x,z)=J(x)+\delta_{(-\infty,0]}(r(x)-\sigma-z)$, using an <indicator functional>. The resulting <convex perturbation duality> expresses multipliers as supporting <subgradients> of the value function.
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