Solving nonlinear financial planning problems
with 109 decision variables
on massively parallel architectures

Technical Report MS 2006-002

J. Gondzio and A. Grothey

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 make sthese problems potentially tractable, but is generally not exploited in todays general purpose solvers. We apply a structure-exploiting parallel primal-dual interior-point solver for linear, quadratic and nonlinear programming problems. The solver efficiently exploitats 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 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.

Key words: Asset and Liability Management, Interior Point Methods,
Massive Parallelism, Structure Exploitation

PDF MS06-002.pdf.
Written: March 8, 2006.
Published: M. Costantino, C.A. Brebbia (eds.), Computational Finance and its Applications II, WIT Transactions on Modelling and Simulation, 43, WIT Press, 2006.
Related Software:
OOPS Object-Oriented Parallel Solver.