Source code for cr.sparse._src.fom.dantzig_scd

# Copyright 2021 CR-Suite Development Team
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# Licensed under the Apache License, Version 2.0 (the "License");
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#     https://www.apache.org/licenses/LICENSE-2.0
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"""
First Order Solver for Dantzig selector problem
"""

from jax import jit

import cr.sparse.opt as opt
import cr.sparse.lop as lop

from .scd import scd
from .defs import FomOptions


def dantzig_scd(A, b, delta, mu, x0, z0, options: FomOptions = FomOptions()):
    r"""Solver for the (smoothed) Dantzig selector problem using smoothed conic dual formulation


    Args:
        A (cr.sparse.lop.Operator): A linear operator 
        b (jax.numpy.ndarray): The measurements :math:`b \approx A x`
        delta (float): An upper bound on the correlation of columns of A with the residual
        mu (float): The (positive) scaling term for the quadratic term :math:`\frac{\mu}{2} \| x - x_0 \|_2^2` 
        x0 (jax.numpy.ndarray): The center point for the quadratic term
        z0 (jax.numpy.ndarray): The initial dual point 
        options (FomOptions): Options for configuring the algorithm

    Returns: 
        FomState: Solution of the optimization problem

    We consider the optimization problem 

    .. math::

        \begin{aligned}
            & \underset{x}{\text{minimize}} 
            & &  \| x \|_1  + \frac{\mu}{2} \| x - x_0 \|_2^2\\
            & \text{subject to}
            & &  \| A^* (y - A x ) \|_{\infty} \leq \delta
        \end{aligned}
    """
    prox_f = opt.prox_l1()
    conj_neg_h = opt.prox_l1(delta)
    G = lop.gram(A)
    bb = -A.trans(b)
    sol = scd(prox_f, conj_neg_h, G, bb, mu, x0, z0, options)
    return sol