J. Gondzio and A. Grothey
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 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