cr.sparse.opt.indicator_l2_ball

cr.sparse.opt.indicator_l2_ball(q=1.0, b=None, A=None)[source]

Returns an indicator function for the closed ball \(\| A x - b \|_2 \leq q\)

Parameters

  • q (float) – Radius of the ball

  • b (jax.numpy.ndarray) – A vector \(b \in \RR^{m}\)

  • A (jax.numpy.ndarray) – A matrix \(A \in \RR^{m \times n}\)

Returns

An indicator function

The indicator function is defined as:

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

Special cases:

  • indicator_l2_ball() returns the Euclidean unit ball \(\| x \|_2 \leq 1\).

  • indicator_l2_ball(q) returns the Euclidean ball \(\| x \|_2 \leq q\).

  • indicator_l2_ball(q, b=b) returns the Euclidean ball at center \(b\), \(\| x - b\|_2 \leq q\).

Notes:

  • If center \(b \in \RR^m\) is unspecified, we assume the center to be at origin.

  • If radius \(q\) is unspecified, we assume the radius to be 1.

  • If the matrix \(A\) is unspecified, we assume \(A\) to be the identity matrix \(I \in \RR^{n \times n}\).