In a finite dimensional (think Euclidean) ambient space, let $S$ a compact, convex set and $x$ not in $S$. The two sets can be (weakly) separated, i.e. there exists a vector (normal) that defines a hyperplane separating the point and the set. In fact, there exists an entire (open) set of normals that separate the point and the set. How can one describe this set?
Describing a set of normals
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convex-analysis
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0Perhaps this will help http://en.wikipedia.org/wiki/Separating_axis_theorem – 2011-01-12
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0@Trevor: thank you. It seems to me that it is a re-iteration of the question on the "primal" space. – 2011-01-12