# cr.sparse.fom.owl1rls¶

cr.sparse.fom.owl1rls(A, b, lambda_, x0, 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 ordered weighted l1 norm regulated least square problem

Parameters
• A (cr.sparse.lop.Operator) – A linear operator

• b (jax.numpy.ndarray) – The measurements $$b \approx A x$$

• lambda (jax.numpy.ndarray) – A strictly positive weight vector which is sorted in decreasing order

• x0 (jax.numpy.ndarray) – Initial guess for solution vector

• options (FomOptions) – Options for configuring the algorithm

Returns

Solution of the optimization problem

Return type

FomState

The ordered weighted l1 regularized least square problem is defined as:

(1)$\underset{x \in \RR^n}{\text{minimize}} \frac{1}{2} \| A x - b \|_2^2 + \sum_{i=1}^n \lambda_i | x |_{(i)}$

The ordered weighted $$\ell_1$$ norm of $$x$$ w.r.t. the weight vector $$\lambda$$ is defined as:

(2)$J_{\lambda} (x) = \sum_{1}^n \lambda_i | x |_{(i)}$

See also

cr.sparse.opt.prox_owl1() for details about the ordered weighted l1 norm.