cr.sparse.fom.owl1rls_jit(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))

Solver for ordered weighted l1 norm regulated least square problem

  • 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


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.