Given a feasibility problem with both inequality and equality constraints, I'm interested in the sensitivity of the bounds of the region to changes in the constraints. To help with answering the rather general question, I'm interested in particular for linear equality constraints with perturbations for
- Linear
- Non-linear
inequality constraints. As a sample problem, consider
$$ \begin{align} min \qquad 1 \\ \text{subject to} \hspace{1ex} b-\epsilon \leq \hspace{1ex}&a^{T}x \leq b + \epsilon \\ \mathbf{1}^{T}x &= 1 \end{align} $$
How do the limits of each co-ordinate in the feasible region $x_{i}$ vary as a function of $\epsilon$? Is there a common name for this problem?