Decentralized proximal splitting algorithms for composite constrained convex optimization

This paper concentrates on a class of decentralized convex optimization problems subject to local feasible sets, equality and inequality constraints, where the global objective function consists of a sum of locally smooth convex functions and non-smooth regularization terms. To address this problem, a synchronous full-decentralized primal-dual proximal splitting algorithm (Syn-FdPdPs) is presented, which avoids the unapproximable property of the proximal operator with respect to inequality constraints via logarithmic barrier functions. Following the proposed decentralized protocol, each agent carries out local information exchange without any global coordination and weight balancing strategies introduced in most consensus algorithms. In addition, a randomized version of the proposed algorithm (Rand-FdPdPs) is conducted through subsets of activated agents, which further removes the global clock coordinator. Theoretically, with the help of asymmetric forward-backward-adjoint (AFBA) splitting technique, the convergence results of the proposed algorithms are provided under the same local step-size conditions. Finally, the effectiveness and practicability of the proposed algorithms are demonstrated by numerical simulations on the least-square and least absolute deviation problems. (C) 2022 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.

Automated summary

This paper focuses on a class of decentralized convex optimization problems and introduces a synchronous full-decentralized primal-dual proximal splitting algorithm and its randomized version. The problems are solved through local information exchange without global coordination, and the convergence results are obtained with the help of asymmetric forward-backward-adjoint splitting technique. Numerical simulations demonstrate the effectiveness and practicability of the algorithms.