Basis Pursuit solver for the \(P_1\) problem
(1)\[\min_x \|x\|_1 \quad \text{s.t.} \ \boldsymbol{A} \vec{x} = \vec{b}\]
via linear programming.
scipy.optimize.linprog is used to solve the linear programming task.
- Parameters
- A(N, M) np.ndarray
The input weight matrix \(\boldsymbol{A}\).
- b(N,) np.ndarray
The right side of the equation (1).
- tolfloat
The accuracy tolerance of linprog.
- Returns
- x(M,) np.ndarray
\(\vec{x}\), the solution to (1).