# American Institute of Mathematical Sciences

July  2020, 16(4): 1655-1662. doi: 10.3934/jimo.2019022

## A new interpretation of the progressive hedging algorithm for multistage stochastic minimization problems

 1 School of Electric Engineering, Computing, and Mathematical Science, Curtin University, Australia 2 School of Business, National University of Singapore 3 School of Electric Engineering, Computing, and Mathematical Science, Curtin University, Australia

* Corresponding author: Min Zhang

Received  August 2018 Published  March 2019

The progressive hedging algorithm of Rockafellar and Wets for multistage stochastic programming problems could be viewed as a two-block alternating direction method of multipliers. This correspondence brings in some useful results. In particular, it provides a new proof for the convergence of the progressive hedging algorithm with a flexibility in the selection of primal and dual step lengths and it helps to develop a new progressive hedging algorithm for solving risk averse stochastic optimization problems with cross constraints.

Citation: Jie Sun, Honglei Xu, Min Zhang. A new interpretation of the progressive hedging algorithm for multistage stochastic minimization problems. Journal of Industrial & Management Optimization, 2020, 16 (4) : 1655-1662. doi: 10.3934/jimo.2019022
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