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web.stanford.edu– primalfeasibility: Ax +Bz − c =0 – dualfeasibility: ∇f(x)+ATy =0, ∇g(z)+BTy =0 since zk+1 minimizes L ρ(xk+1,z,yk) we have 0 = ∇g(zk+1)+BTyk +ρBT(Axk+1 +Bzk+1 −c) = ∇g(zk+1)+BTyk+1 so with ADMM dual variable update, (xk+1,zk+1,yk+1) satisfies second dual feasibility condition
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