Solving nonlinear financial planning problems with 10 9 decision variables on massively parallel architectures

Abstract

Multistage stochastic programming is a popular technique to deal with uncertainty in optimization models. However, the need to adequately capture the underlying distributions leads to large problems that are usually beyond the scope of general purpose solvers. Dedicated methods exist but pose restrictions on the type of model they can be applied to. Parallelism makes these problems potentially tractable, but is generally not exploited in today's general purpose solvers. We apply a structure-exploiting parallel primal-dual interior-point solver for linear, quadratic and nonlinear programming problems. The solver efficiently exploits the structure of these models. Its design relies on object-oriented programming principles, treating each substructure of the problem as an object carrying its own dedicated linear algebra routines. We demonstrate its effectiveness on a wide range of financial planning problems, resulting in linear, quadratic or non-linear formulations. Also coarse grain parallelism is exploited in a generic way that is efficient on any parallel architecture from ethernet linked PCs to massively parallel computers. On a 1280-processor machine with a peak performance of 6.2 TFlops we can solve a quadratic financial planning problem exceeding 109 decision variables.