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

@article{Gade2016ObtainingLB,
  title={Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs},
  author={Dinakar Gade and Gabriel Hackebeil and Sarah M. Ryan and Jean-Paul Watson and Roger J.-B. Wets and David L. Woodruff},
  journal={Math. Program.},
  year={2016},
  volume={157},
  pages={47-67}
}
We present a method for computing lower bounds in the Progressive Hedging Algorithm (PHA) for two-stage and multi-stage stochastic mixedinteger 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 show that the best possible lower bound obtained using dual prices… CONTINUE READING
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