An O(1/k) algorithm for multi-agent optimization with inequality constraints

Abstract

This paper presents a discrete-time solution algorithm for a constrained multi-agent optimization problem with inequality constraints. Its aim is to seek a solution to minimize the sum of all the agents’ objective functions while satisfy each agent’s local set constraint and nonlinear inequality constraints. Assume that agents’ local constraints are heterogeneous and all the objective functions are convex and continuous, but they may not be differentiable. Similar to the distributed alternating direction method of multipliers (ADMM) algorithm, the designed algorithm can solve the multi-agent optimization problem in a distributed manner and has a fast $O(1/k)$ convergence rate. Moreover, it can deal with the nonlinear constraints, which cannot be handled by distributed ADMM algorithm. Finally, the proposed algorithm is applied to solve a robust linear regression problem, a lasso problem and a decentralized joint flow and power control problem with inequality constraints, respectively and thus the effectiveness of the proposed algorithm is verified.