cr.sparse.opt.indicator_conic

cr.sparse.opt.indicator_conic()

Returns an indicator function for Lorentz/ice-cream cone \({(x,t): \| x \|_2 \leq t}\)

Let \(y \in \RR^{n+1}\). Split \(y\) as \(y = (x, t)\) where \(x \in \RR^n\) and \(t\) is the last (scalar) entry in \(y\).

We then define the convex set \(C \subset \RR^{n+1}\) as \(C = \{ y = (x,t) : \; \|x \|_2 \leq t \}\).

The indicator function is defined as:

(1)\[\begin{split}I((x,t)) = \begin{cases} 0 & \text{if } \| x \|_2 \leq t \\ \infty & \text{otherwise} \end{cases}\end{split}\]

The ice-cream cone doesn’t include any point with \(t \lt 0\).