Parallel algorithms to solve two-stage stochastic linear programs with robustness constraints

In this paper we present a parallel method for solving two-stage stochastic linear programs with restricted recourse. The mathematical model considered here can be used to represent several real-world applications, including financial and production planning problems, for which significant changes in the recourse solutions should be avoided because of their difficulty to be implemented. Our parallel method is based on a primal-dual path-following interior point algorithm, and exploits fruitfully the dual block-angular structure of the constraint matrix and the special block structure of the matrices involved in the restricted recourse model. We describe and discuss both message-passing and shared-memory implementations and we present the numerical results collected on the Origin2000.