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Integration of progressive hedging and dual decomposition in stochastic integer programs

Watson, Jean-Paul W.; Guo, Ge; Hackebeil, Gabriel; Ryan, Sarah M.; Woodruff, David L.

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. As a result, we report computational results on server location and unit commitment instances.