[PAST EVENT] Mathematics Colloquium and EXTREEMS-QED Lecture: Yongjia Song (VCU)
April 15, 2016
2pm - 3pm
Abstract: In this talk, we first briefly review the background of stochastic programming as well as the state-of-the-art solution methodology for stochastic programs. We will then focus on a recently proposed solution framework, the adaptive partition-based framework, for solving two-stage stochastic programs with fixed recourse. A partition-based formulation is a relaxation of the original stochastic program, and we study a finitely converging algorithm in which the partition is adaptively adjusted until it yields an optimal solution. A solution guided refinement strategy is developed to refine the partition by exploiting the intermediate relaxation solutions obtained from a partition. We also show that for stochastic linear programs with fixed recourse, there exists a partition that yields an optimal solution, whose size is independent of the number of scenarios. Computational results show that the proposed approach is competitive with the state-of-art methods for stochastic linear programs. In particular, our numerical experiments show that stochastic programs with up to a million scenarios can be solved efficiently.