A Revisit of Chen-Teboulle's Proximal-based Decomposition Method

In this paper, we show that Chen-Teboulle’s proximal-based decomposition method can be interpreted as a proximal augmented Lagrangian method. More precisely, it coincides with a linearized augmented Lagrangian method. We then proposed three generalized methods based on this interpretation. By invoking recent work (He et al., IMA J. Numer. Anal., 32 (2020), pp. 227–245), we show that the step size condition of Chen-Teboulle’s method can be relaxed without adding any further assumptions. Our analysis offers a new insight into this proximal-based decomposition method.