| | |
Summary: Optimization Methods and Software
Vol. 00, No. 00, Month 200x, 120
RESEARCH ARTICLE
On the parallel solution of dense saddle-point linear systems
arising in stochastic programming
Miles Lubin, Cosmin G. Petra
and Mihai Anitescu
Mathematics and Computer Science Division, Argonne National Laboratory, IL, USA
(released October 15, 2010)
Preprint ANL/MCS-P1798-1010
We present a novel approach for solving dense saddle-point linear systems in a distributed-
memory environment. This work is motivated by an application in stochastic optimization
problems with recourse, but the proposed approach can be used for a large family of dense
saddle-point systems, in particular those arising in convex programming. Although stochastic
optimization problems have many important applications, they can present serious computa-
tional difficulties. In particular, sample average approximation (SAA) problems with a large
number of samples are often too big to solve on a single shared-memory system. Recent work
has developed interior point methods and specialized linear algebra to solve these problems
in parallel, using a scenario-based decomposition that distributes the data and work across
computational nodes. Even for sparse SAA problems, the decomposition produces a dense and
|
