Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs

Date
2016-05-01
Authors
Gade, Dinakar
Hackebeil, Gabriel
Ryan, Sarah
Ryan, Sarah
Watson, Jean-Paul
Wets, Roger
Woodruff, David
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Ryan, Sarah
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Abstract

We present a method for computing lower bounds in the progressive hedging algorithm (PHA) for two-stage and multi-stage stochastic mixed-integer programs. Computing lower bounds in the PHA allows one to assess the quality of the solutions generated by the algorithm contemporaneously. The lower bounds can be computed in any iteration of the algorithm by using dual prices that are calculated during execution of the standard PHA. We report computational results on stochastic unit commitment and stochastic server location problem instances, and explore the relationship between key PHA parameters and the quality of the resulting lower bounds.

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<p>This is a manuscript of an article from <em>Mathematical Programming</em>, Series B, 157 (2016): 47, doi: <a href="http://dx.doi.org/10.1007/s10107-016-1000-z." target="_blank">10.1007/s10107-016-1000-z.</a> The final publication is available at Springer via http://dx.doi.org/1<a href="http://dx.doi.org/10.1007/s10107-016-1000-z." target="_blank">0.1007/s10107-016-1000-z</a>.</p>
Keywords
Stochastic mixed-integer programming, Decomposition algorithms, Lower bounding
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