Industrial and Manufacturing Systems Engineering
Journal or Book Title
Mathematical Programming, Series B
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.
Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society
Gade, Dinakar; Hackebeil, Gabriel; Ryan, Sarah M.; Watson, Jean-Paul; Wets, Roger J-B; and Woodruff, David L., "Obtaining lower bounds from the progressive hedging algorithm for stochastic mixed-integer programs" (2016). Industrial and Manufacturing Systems Engineering Publications. 73.