表示為點雲的可行集


3

是否存在優化問題,即問題中沒有用顯式代數方程式描述可行集,而是有大量近似於可行集的點?如果是這樣,是否有專門的術語?

在我的特殊情況下,我知道有很多樣本是可行的,並且自然要做的是用一些固定半徑的球包圍它們,然後將它們的並集用作我的可行集合。我想知道這是否正在深入研究一些優化領域。

3

I don't think I've ever seen a name (let alone any research) for the case of having a collection of known feasible points but no explicit mathematical criteria for feasibility.

Before gluing together a bunch of balls, I would first ask whether the nature of the problem tells you anything about the shape of the feasible region. I'm assuming that your variables are not discrete, since the union of balls thing would not make sense for integer-valued variables (the union would contain non-integral points). Does the problem lead you to expect a convex feasible region? If so, the convex hull of your known feasible points would be a subset of the true feasible region (with no way of knowing how much of the feasible region you had not captured). If not convex, is there anything else you know about the feasible region based on the problem?