cr.sparse.fom.dantzig_scd¶
- cr.sparse.fom.dantzig_scd(A, b, delta, mu, x0, z0, options=FomOptions(nonneg=False, solver='at', max_iters=1000, tol=1e-08, L0=1.0, Lexact=inf, alpha=0.9, beta=0.5, mu=0, maximize=False, saddle=False))[source]¶
Solver for the (smoothed) Dantzig selector problem using smoothed conic dual formulation
- Parameters
A (cr.sparse.lop.Operator) – A linear operator
b (jax.numpy.ndarray) – The measurements \(b \approx A x\)
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 \(\frac{\mu}{2} \| x - x_0 \|_2^2\)
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
Solution of the optimization problem
- Return type
We consider the optimization problem
(1)¶\[\begin{split}\begin{aligned} & \underset{x}{\text{minimize}} & & \| x \|_1 + \frac{\mu}{2} \| x - x_0 \|_2^2\\ & \text{subject to} & & \| A^* (y - A x ) \|_{\infty} \leq \delta \end{aligned}\end{split}\]
