Infeasibility

[klamike]

When all primal variables have bounds, the BoundDecomposition completion is always feasible. When all primal variables have quadratic terms, the ConvexQP completion is always feasible. Besides those, there is no guarantee of feasibility for the completion problem. In the generic case, we throw an error, but in the others the objective reported is (silently) infeasible. We should detect infeasibility and throw an error in that case, for now.

Eventually, it may be nice to explore some strategies for getting around the infeasibility, for example instead of solving

$$\max_{z} b^\top \hat{y} + h^\top z \quad \text{s.t.} \quad A^\top \hat{y} + H^\top z = c,\quad z\in\mathcal{C}^\ast$$

we can solve

$$\max_{y, z} b^\top y + h^\top z - \alpha\Vert y-\hat{y}\Vert \quad \text{s.t.} \quad A^\top y + H^\top z = c,\quad z\in\mathcal{C}^\ast$$