Proximal nested primal-dual gradient algorithms for distributed constraint-coupled composite optimization.

• The proposed Prox-NPGA can handle the non-smooth term in the objective function. • The convergences of CTA-Prox-NPGA and ATC-Prox-NPGA are proved. • The upper bounds of the step-sizes are given. • Prox-NPGA is not only an algorithm, but also an algorithmic framework. In this paper, we study a class of distributed constraint-coupled optimization problems, where each local function is composed of a smooth and strongly convex function and a convex but possibly non-smooth function. We design a novel proximal nested primal-dual gradient algorithm (Prox-NPGA), which is a generalized version of the exiting algorithm–NPGA. The convergence of Prox-NPGA is proved and the upper bounds of the step-sizes are given. Finally, numerical experiments are employed to verify the theoretical results and compare the convergence rates of different versions of Prox-NPGA. [ABSTRACT FROM AUTHOR]