Adapting Progressive Hedging for Solving Two-Stage Stochastic Programs Under a Peer-to-Peer Computing Network

Following recent technology advances and increasing applications in peer-to-peer network computing, we explore the potential of using decentralized optimization methods to solve notoriously hard stochastic programs. As the first attempt, we adapt the well-known progressive hedging (PH) method under a peer-to-peer computing network for solving two-stage stochastic programs efficiently. Similar to the existing parallel PH method, our decentralized variant assigns each node within the network to take charge of the computing tasks covering one or few scenarios, and thus it distributes the overall computational burden over the entire network. However, unlike the parallel PH method, the decentralized variant no longer needs a master node to realize central coordination, and thus it improves the scalability of the network computing as well. In this paper, we show the exact convergence of our decentralized method for solving two-stage stochastic programs with continuous variables subject to convex constraints. Further, we investigate several computational issues for the mixed-integer cases to improve the adaptation efficiency. Finally, the efficiency of our method is demonstrated through comparative computational experiments on a set of benchmark test instances.