cr.sparse.fom.l1rls(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 l1 regulated least square problem

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

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

  • lambda (float) – The regularization parameter for the l1 term

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

  • options (FomOptions) – Options for configuring the algorithm


Solution of the optimization problem

Return type


The l1 regularized least square problem is defined as:

(1)\[\text{minimize} \frac{1}{2} \| A x - b \|_2^2 + \lambda \| x \|_1\]

Sometimes, this is also called LASSO in literature.