A Fixed Step-Size Algorithm for Distributed Optimization With Both Globally Coupled and Locally Separated Constraints

This article proposes a distributed Lagrange alternating gradient descent (LAGD) algorithm with a fixed step size for constrained optimization over a multiagent communication network. Interconnected by multiagent networks, agents optimize their own objective function subject to local constraints cooperatively, and the whole network shares globally coupled constraints. All agents reach consensus on the estimations of multipliers via the network communication to handle the globally coupled constraints, and the decision variable vectors converge to the optimal solution along the Lagrange gradient direction. The convergence of the algorithm is proven under the condition of fixed step sizes subject to a theoretical upper bound. An economic dispatch problem in a power system and a numerical example are elaborated to verify and demonstrate the effectiveness of the algorithm.