Table 1 Regularity conditions to convergence analysis of ADMM for nonconvex optimization problem
M | f, g | KL property | Lyapunov function | |
|---|---|---|---|---|
Hong [14] | M = I | f and g gradient Lipschitz continuous | no | ALF |
Li [15] | full row rank | bounded Hessian of f | yes | ALF |
Wang [16] | full row rank | f gradient Lipschitz continuous g strongly convex | yes | variants of ALF |
Wang [17] | weak full column rank condition | f gradient Lipschitz continuous g has special structure | yes | ALF |
Ours | full column rank | f strongly convex g weakly convex | no | \(H^{k}\) (shown in Sect. 3) |