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
The ordered weighted l1 regularized least square problem [lBvdBSC13] 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.
