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1)Does dual cone define just for proper cone or all kinds of cone ?

2)Can someone show me a figure that shows a dual cone of a cone ? In Convex Optimization by Boyd (P.51) said that " $y\in k^*$ iff $-y$ is the normal of hyperplane that supports $k$ at the origin" what does it mean?

eHH
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1 Answers1

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1) It is defined for all kinds of cone, even for an arbitrary set (see this link for more information).

2) A figure is shown in p. 143 of Dattorro, Jon. Convex optimization & Euclidean distance geometry. Meboo Publishing USA, 2005. For the explanation, see also pp.141-142. Fortunately, all of these pages are available in google books preview.

shamisen
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