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

TL;DR

This paper reinterprets Chen-Teboulle's proximal decomposition method as a linearized augmented Lagrangian approach, introduces generalized variants, and relaxes step size conditions, providing new theoretical insights.

Contribution

It offers a novel interpretation of Chen-Teboulle's method and proposes generalized methods with relaxed step size constraints based on recent theoretical developments.

Findings

Chen-Teboulle's method is equivalent to a linearized augmented Lagrangian method.

Three generalized methods are proposed based on this interpretation.

Step size conditions can be relaxed without additional assumptions.

Abstract

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.