Dual cone and polar cone http://en.wikipedia.org/wiki/Dual_cone_and_polar_cone are defined only on $\mathbb R^n$. Has anyone seen the extension to $\mathbb C^n$? Any references for these?
Dual cone and polar cone
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optimization
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0@Sunni: If $z_1=a_1+ib_1$ and $z_2=a_2+ib_2$, then we define $z_1 \cdot z_2 = a_1 a_2+b_1b_2$. You can check that this gives the absolute value squared when $z_1=z_2$. – 2011-12-19
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As I see it, the definition in Wikipedia is for any Linear Space. The book by Aliprantis and Border defines polars for any Dual Set, which is even more general. These general definitions are very useful in Convex Optimization, but I've never seen it used on $\mathbb{C}^n$.