A Optimization Convergence Rate for CLIME ADMM

All norms in this section are defined elementwise. To recap, we solve the following problem: min ‖X‖1 s.t. ‖Z−E‖ ∞ ≤ λ,CX = Z. (1) The Lagrangian of (1) is L(X,Z,Y) = ‖X‖1 + ρ〈Y,CX − Z 〉 , (2) where ‖Z−E‖ ∞ ≤ λ. Assume that {X∗,Z∗,Y∗} satisfies the KKT conditions of (2), i.e., −ρCTY ∗ ∈ ∂‖X∗‖1, (3