A New Decomposition Technique in Solving Multistage Stochastic Linear Programs by Infeasible Interior Point Methods

Multistage stochastic linear programming (MSLP) is a powerful tool for making decisions under uncertainty. A deteministic equivalent of MSLP is a large-scale linear program with nonanticipativity constraints. Recently developed infeasible interior point methods are used to solve the resulting linear program. Technical problems arising from this approach include rank reduction and computation of search directions. In particular, the search direction is generated by solving a set of primal-dual equations with size much less than the original problem. The sparsity and special structure of the problem are exploited by the interior point method. Preliminary numerical results are reported. The study shows that, by combining the infeasible interior points and specific decomposition techniques, it is possible to greatly improve the computability of multistage stochastic linear programs.