Ok, so, I have a function $f_I(y_1, y_2) = \max\{\alpha y_1 + (1-\alpha)y_2:\alpha\in[\alpha_{min},\alpha_{max}]\}$ that I'm trying to minimise, and I'm asked to find, amongst a set of vectors $y$, the vectors that aren't Pareto-dominated.
Except... I have no idea what a non-Pareto-dominated vector is in this case.
And yes, that's really all I have to go on. The instructions are on this link (it's a pdf in French). I'm told that a vector is non-dominated if there is no other vector that strictly dominates it (regardless of the interval $I$), but I don't know what that condition entails.
Um... help?
In this case, it appears what the problem description meant was exactly that $y$ is non-Pareto-dominated if there is no $y'$ such that $y'$ Pareto-dominates $y$.