adelie.bcd.root_lower_bound#

adelie.bcd.root_lower_bound(*, quad: ndarray, linear: ndarray, l1: float)[source]#

Computes a lower bound on the root of BCD root function.

The lower bound \(h_\star\) is guaranteed to be non-negative and satisfies \(\varphi(h_\star) \geq 0\) where \(\varphi\) is given by adelie.bcd.root_function() whenever \(\|v\|_2 > \lambda\). It is undefined behavior if the condition is not satisfied.

Parameters:

quad(p,) ndarray: See adelie.bcd.root_function().
linear(p,) ndarray: See adelie.bcd.root_function().
l1float: See adelie.bcd.root_function().

Returns:

lowerfloat: Lower bound on the root.