Convex Optimization based Sparse Recovery/Approximation Algorithms

Alternating Directions Methods

A tutorial has been provided to explore these methods in action. The yall1.solve method is an overall wrapper method for solving different types of \(\ell_1\) minimization problems. It in turn calls the lower level methods for solving specific types of problems.

yall1.solve(A, b[, x0, z0, W, weights, …])	Wrapper method to solve a variety of l1 minimization problems using ADMM
yall1.solve_bp(A, b, x0, z0, w, nonneg, …)	Solves the problem \(\min \| x \|_1 \text{s.t.} \A x = b\) using ADMM
yall1.solve_bp_jit(A, b, x0, z0, w, nonneg, …)	Solves the problem \(\min \| x \|_1 \text{s.t.} \A x = b\) using ADMM
yall1.solve_l1_l2(A, b, x0, z0, w, nonneg, …)	Solves the problem \(\min \| x \|_1 + \frac{1}{2 \rho} \| A x - b \|_2^2\) using ADMM
yall1.solve_l1_l2_jit(A, b, x0, z0, w, …)	Solves the problem \(\min \| x \|_1 + \frac{1}{2 \rho} \| A x - b \|_2^2\) using ADMM
yall1.solve_l1_l2con(A, b, x0, z0, w, …)	Solves the problem \(\min \| x \|_1 \text{s.t.} \| A x - b \|_2 \leq \delta\) using ADMM
yall1.solve_l1_l2con_jit(A, b, x0, z0, w, …)	Solves the problem \(\min \| x \|_1 \text{s.t.} \| A x - b \|_2 \leq \delta\) using ADMM