Algorithm 3.

The accelerated iterative shrinkage thresholding algorithm (AISTA). Within each iteration, we exploit an additional coordinate descent subroutine to improve the empirical computational performance.

Algorithm: {θ̂, L̂} ← AISTA(λ, θ[0], L[0])

Initialize: m ← 0

Repeat:

z ← 0

Repeat:

L [m+1] ← 2z L[m], θ[m+0.5] ← 𝒯λ,Ω,L[m+1] (θ[m]), z ← z + 1

Until: 𝒬λ,L[m+1] (θ[m+0.5]; θ[m]) ≥ ℱλ(θ[m+1])

θ[m+1] ← CCDA(λ, θ[m+0.5]), m ← m + 1

Until convergence

θ̂ ← θ[m−0.5], L̂ ← L[m]

Output: {θ̂, L̂}