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For a set <math>C</math> in <math>X</math>, the '''polar cone''' of <math>C</math> is the set
:<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=9780691015866|pages=121-122}}</ref>
It can be seen that the polar cone cone is equal to the negative of the dual cone, i.e. <math>C^o=-C^*</math>.
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