Integration of progressive hedging and dual decomposition in stochastic integer programs

Date
2015-05-01
Authors
Guo, Ge
Hackebeil, Gabriel
Ryan, Sarah
Watson, Jean-Paul
Woodruff, David
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Ryan, Sarah
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Abstract

We present a method for integrating the Progressive Hedging (PH) algorithm and the Dual Decomposition (DD) algorithm of Carøe and Schultz for stochastic mixed-integer programs. Based on the correspondence between lower bounds obtained with PH and DD, a method to transform weights from PH to Lagrange multipliers in DD is found. Fast progress in early iterations of PH speeds up convergence of DD to an exact solution. We report computational results on server location and unit commitment instances.

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NOTICE: this is the author's version of a work that was accepted for publication in Operation Research Letters. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Operations Research Letters, [v.43, iss.3,(2015)]. DOI: 10.1016/j.orl.2015.03.0

Keywords
Stochastic programming, Mixed-integer programming, Progressive hedging, Dual decomposition, Lower bounding
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