This note presents not only a surrogate subgradient method, but also a framework of surrogate subgradient methods. Furthermore, the framework can be used not only for separable problems, but also for coupled subproblems. The note delineates such a framework and shows that the algorithm can converges for a larger stepsize.
Guan, X.H., Zhai, Q.Z., Lai, F.: New Lagrangian relaxation based algorithm for resource scheduling with homogeneous subproblems. J. Optim. Theory Appl. 113(1), 65–82 (2002)