Perturbation function

In mathematical optimization, the perturbation function is any function which relates to primal and dual problems. The name comes from the fact that any such function defines a perturbation of the initial problem. In many cases this takes the form of shifting the constraints.

In some texts the value function is called the perturbation function, and the perturbation function is called the bifunction.

Given two dual pairs separated locally convex spaces ${\displaystyle \left(X,X^{*}\right)}$ and ${\displaystyle \left(Y,Y^{*}\right)}$. Then given the function ${\displaystyle f:X\to \mathbb {R} \cup \{+\infty \}}$, we can define the primal problem by

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