Dual cone and polar cone: Difference between revisions

Revision as of 22:19, 22 May 2020

Revision as of 22:21, 22 May 2020

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:<math>C^* = \left \{y\in X^*: \langle y , x \rangle \geq 0 \quad \forall x\in C \right \},</math>

where <math>\langle y, x \rangle</math> is the [[dual system|duality pairing]] between ''X'' and ''X{{sup|*}}'', i.e. <math>\langle y, x\rangle = y(x)</math>.

''C{{sup|*}}'' is always a [[convex cone]], even if ''C'' is neither [[convex set|convex]] nor a [[linear cone|cone]].