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Moved alternative definition of dual to follow existing one. Clarified that the conditions from Boyd & Vandenberghe assume this alternative definition. |
m →Polar cone: Typo fixing, replaced: cone cone → cone using AWB (8323) |
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:<math>C^o = \left \{y\in X^*: \langle y , x \rangle \leq 0 \quad \forall x\in C \right \}.</math><ref name="Rockafellar">{{cite book|author=[[Rockafellar, R. Tyrrell]]|title=Convex Analysis|publisher=Princeton University Press|___location=Princeton, NJ|year=1997|origyear=1970|isbn=978-0-691-01586-6|pages=121-122}}</ref>
It can be seen that the polar
For a closed convex cone <math>C</math> in <math>X</math>, the polar cone is equivalent to the [[polar set]] for <math>C</math>.<ref>{{cite book|last=Aliprantis|first=C.D.|last2=Border|first2=K.C.|title=Infinite Dimensional Analysis: A Hitchhiker's Guide|edition=3|publisher=Springer|year=2007|isbn=978-3-540-32696-0|doi=10.1007/3-540-29587-9|page=215}}</ref>
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