On the implementation of a log-barrier progressive hedging method for multistage stochastic programs

A progressive hedging method incorporated with self-concordant barrier functions has been developed by Zhao [23] for solving multistage stochastic programs. The method relaxes the nonanticipativity constraints by the Lagrangian dual approach and smooths the Lagrangian dual function by self-concordant barrier functions. This paper discusses in detail the implementation of this method and reports results of preliminary numerical experiments. We compare the performance of this method with the well-known progressive hedging method proposed by Rockafellar and Wets [17]. keywords: Progressive hedging method, multistage stochastic programs, Lagrangian dual, log-barrier method, ∗Research is partially supported by NUS Academic Research Grant R-146-000-006-112 †This author is on leave from Hebei University of Technology, Tianjin, China. The research is partially supported by SRF for ROCS, SEM. ‡Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543. Email: [email protected]. §Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore 117543. Email: [email protected].