A revisit of chen-teboulle's proximal-based decomposition method

. The predictor corrector proximal multiplier method (PCPM) proposed by Chen and Teboulle in early 1990s is a popular scheme for linearly constrained composite minimization problems. In this paper, we show that the PCPM is equivalent to a special case of the linearized augmented Lagrangian method (ALM). Using this interpretation, we identify the necessary and sufficient convergence condition for its convergence. As a byproduct, the stepsize condition of Chen-Teboulle's PCPM can be improved without adding any further assumptions. We prove the global convergence of the PCPM with this improved condition. We also propose a generalized version of PCPM with convergence guarantee under mild conditions.