Primal-Dual Algorithm for Distributed Constrained Optimization

Jinlong Lei, Han-Fu Chen, Hai-Tao Fang

Published 2015-10-29Version 1

This paper studies the distributed optimization problem, where multiple agents connected in a network collectively minimize the sum of individual objective functions subject to a global constraint being an intersection of the local constraint sets assigned to the agents. Based on the augmented Lagrange technique, a primal-dual algorithm with a projection operation included is proposed to solve the problem. It is found that with appropriately chosen constant step-size, the estimates derived at all agents finally reach the consensus: they all tend to the optimal solution. In addition, the value of the cost function at the time-averaged estimate converges to the optimal value at the rate $O(\frac{1}{k})$ for the case where there is no constraint. By these properties the proposed primal-dual algorithm is distinguished from the existing algorithms for the deterministic constrained optimization. The theoretical analysis is justified by the numerical simulation.