Relaxation algorithms

Basis Pursuit (BP) solvers tackle the original \(P_0\) problem (1) by posing L1-relaxation on the norm of unknown \(\vec{x}\).

basis_pursuit_linprog(A, b[, max_iters])	Basis Pursuit solver for the \(P_1\) problem
basis_pursuit_admm(A, b, lambd[, tol, ...])	Basis Pursuit solver for the \(Q_1^\epsilon\) problem

Iterative Shrinkage Algorithm (ISTA) is also used to find an approximate solution to the \(\text{P}_0\) problem though Basis Pursuit methods are superior.

ista(A, b, lambd[, tol, max_iters, momentum])

Iterative Shrinkage Algorithm (ISTA) [Ree9f4f0c3080-1] for the \(Q_1^\epsilon\) problem:

Shrinkage functions.

soft_shrinkage(x, lambd)

Applies the soft shrinkage function elementwise: