adelie.solver.pinball#

adelie.solver.pinball(A: ndarray | MatrixConstraintBase32 | MatrixConstraintBase64, S: ndarray, v: ndarray, penalty_neg: ndarray, penalty_pos: ndarray, *, kappa: int | None = None, max_iters: int = 100000, tol: float = 1e-07, n_threads: int = 1, warm_start=None)[source]#

Solves pinball least squares.

The pinball least squares is given by

\begin{aligned} {minimize}_{β} & \frac{1}{2} ‖ S^{- \frac{1}{2}} v - S^{\frac{1}{2}} A^{⊤} β ‖_{2}^{2} + ℓ^{⊤} β_{-} + u^{⊤} β_{+} \end{aligned}

where $A \in R^{m \times d}$ is a constraint matrix, $S \in R^{d \times d}$ is a positive semi-definite matrix, $v \in R^{d}$ is the linear term, and $ℓ, u \in R^{m}$ are the penalty factors for the negative and positive parts of $β$ , respectively.

Parameters:

A(m, d) Union[ndarray, MatrixConstraintBase32, MatrixConstraintBase64]: Constraint matrix $A$ . It is typically one of the matrices defined in adelie.matrix submodule.
S(d, d) ndarray: Positive semi-definite matrix $S$ .
v(n,) ndarray: Linear term $v$ .
penalty_neg(m,) ndarray: Penalty $ℓ$ on the negative part of $β$ .
penalty_pos(m,) ndarray: Penalty $u$ on the positive part of $β$ .
kappaint, optional: Violation batching size. If None, it is set to min(m, d). Default is None.
max_itersint, optional: Maximum number of coordinate descents. Default is int(1e5).
tolfloat, optional: Coordinate descent convergence tolerance. Default is 1e-7.
n_threadsint, optional: Number of threads. Default is 1.
warm_startoptional: If no warm-start is provided, the initial solution is set to all zeros. Otherwise, the warm-start is used to extract all necessary state variables. Default is None.

Returns:

state: The resulting state after running the solver.