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I know that the conjugate of an indicator function is its support function. Can someone help determine the the support function of this indicator function? $I(x) = 1$ if $Ax +b \geq 0$ and it is $0$ otherwise.

Prat
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    It is not indicator. Indicators have range ${0,+\infty}$, not ${0,1}$ – max_zorn Mar 07 '18 at 15:53
  • I am referring to the following definition:
    An indicator function or a characteristic function is a function defined on a set X that indicates membership of an element in a subset A of X, having the value 1 for all elements of A and the value 0 for all elements of X not in A. I(x) = 1 if c \in A , =0 otherwise     – Prat Mar 07 '18 at 17:31
  • Your definition does not yield a convex function, so the conjugate of your function is not necessarily a support function. – LinAlg Mar 07 '18 at 17:41
  • Thank you. Do you know what is the conjugate of the indicator function I defined above? – Prat Mar 07 '18 at 18:34
  • Just use the definition to derive it yourself. What would you use it for though? – LinAlg Mar 07 '18 at 18:40
  • Trying to do so. I need to get the conjugate to use in a nonlinear optimization problem. – Prat Mar 07 '18 at 20:00

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