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

Jie Sun; Honglei Xu; Min Zhang

doi:10.3934/jimo.2019022

Article Contents

2020, Volume 16, Issue 4: 1655-1662. Doi: 10.3934/jimo.2019022

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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
^* Corresponding author: Min Zhang

Received: July 31, 2018

Early access: March 2019

Published: May 2020

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Abstract

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.

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Mathematics Subject Classification: 65K10, 65K15, 90C15.

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References

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