adelie.bcd.objective

adelie.bcd.objective(beta: ndarray, *, quad: ndarray, linear: ndarray, l1: float, l2: float)

Computes the BCD objective.

The BCD objective is given by

\[\begin{align*} \frac{1}{2} \beta^\top \Sigma \beta - v^\top \beta + \lambda_1 \|\beta\|_2 + \frac{\lambda_2}{2} \|\beta\|_2^2 \end{align*}\]

where \(\beta \in \mathbb{R}^p\), \(\Sigma \in \mathbb{R}_+^{p\times p}\) diagonal, \(v \in \mathbb{R}^p\), and \(\lambda_i \geq 0\).

Parameters:

beta(p,) ndarray

The value \(\beta\) at which the objective is computed.

quad(p,) ndarray

The quadratic component \(\Sigma\).

linear(p,) ndarray

The linear component \(v\).

l1float

The \(\ell_1\) component \(\lambda_1\).

l2float

The \(\ell_2\) component \(\lambda_2\).

Returns:

objfloat

The BCD objective.