Master problem approximations in Dantzig-Wolfe decomposition of variational inequality problems with applications to two energy market models

In this paper, a modification to Dantzig-Wolfe (DW) decomposition algorithm for variational inequality (VI) problems is considered to alleviate the computational burden and to facilitate model management and maintenance. As proposals from DW subproblems are accumulated in the DW master problem, the solution time and memory requirements are increasing for the master problem. Approximation of the DW master problem solution significantly reduces the computational effort required to find the equilibrium. The approximate DW algorithm is applied to a time of use pricing model with realistic network constraints for the Ontario electricity market and to a two-region energy model for Canada. In addition to empirical analysis, theoretical results for the convergence of the approximate DW algorithm are presented.