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by cochleari_major 2176 days ago
For low dimensions, it might be useful to look at the convex properties of the Pareto front. If a point P is on Pareto front, it is not in the interior of the convex hull of undominated points. In two dimensions, one can compute the convex hull of N points in O(N log N) time. This typically allows for faster Pareto front computation, but not in the worst case.
2 comments

Yeah I'm not sure this works. As far as I can tell the Pareto front doesn't have to be convex and can therefore contain points that are in the interior of the convex hull.

Of course if you accept convex combinations of options then the pareto front is part of the convex hull.

> If a point P is on Pareto front, it is not in the interior of the convex hull of undominated points.

Can you elaborate on what you mean by this? Is this under the assumption of a convex Pareto front? I may be misunderstanding.