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

FomState

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}