Solving Multistage Stochastic Programs with Tree Dissection

One component of every multi-stage stochastic program is a ltration that determines the notion of which random events are observable at each stage of the evolution. Within the context of interior-point methods, we describe an e cient pre-ordering technique, called ltered dissection, that takes advantage of the ltration's structure to dramatically reduce ll-in in the factorization as compared with methods such as the default methods employed by cplex-barrier and loqo. We have implemented this technique as a minor modi cation to loqo, and it produces a roughly 200fold performance improvement. In particular, we have solved a previouslyunsolvable, real-world, 6-stage nancial investment problem having 800K equations and 1,200K variables (and 8,192 points in its sample space) using a single processor SGI workstation. The ltered dissection algorithmapplies in a natural manner to generic (linear and convex) multi-stage stochastic programs. The approach promises to eliminate the need for decomposition algorithms for these classes of applications.