Let S be a nonempty convex set in n with 0 S 1 For every point a S, define the polar set S a x n x 1 xTa yen 0 S a is a nonempty closed set 2 For any finite set of points a1, a2, , am in S, let A be the m Atilde n matrix whose rows are ai The system 72

Question: Let S be a nonempty convex set in n with 0 S. 1. For every point a S, define the polar set S*a = {x

Let S be a nonempty convex set in „œn with 0 ˆ‰ S.
1. For every point a ˆˆ S, define the polar set S*a = {x ˆˆ „œn : ||x|| = 1; xTa ‰¥ 0}. S*a is a nonempty closed set.
2. For any finite set of points {a1, a2, ..., am} in S, let A be the m Ã— n matrix whose rows are ai. The system

72 !

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