Primal-dual interior-point methods
Primal-dual interior-point methods
ScaLAPACK user's guide
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic Scheduling
SIAM Journal on Matrix Analysis and Applications
Decomposition Algorithms for Stochastic Programming on a Computational Grid
Computational Optimization and Applications
Hybrid scheduling for the parallel solution of linear systems
Parallel Computing - Parallel matrix algorithms and applications (PMAA'04)
Direct solution of linear systems of size 109 arising in optimization with interior point methods
PPAM'05 Proceedings of the 6th international conference on Parallel Processing and Applied Mathematics
The parallel solution of dense saddle-point linear systems arising in stochastic programming
Optimization Methods & Software - Special issue in honour of Professor Florian A. Potra's 60th birthday
Parallel distributed-memory simplex for large-scale stochastic LP problems
Computational Optimization and Applications
Turbine: A Distributed-memory Dataflow Engine for High Performance Many-task Applications
Fundamenta Informaticae - Scalable Workflow Enactment Engines and Technology
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We present a scalable approach and implementation for solving stochastic programming problems, with application to the optimization of complex energy systems under uncertainty. Stochastic programming is used to make decisions in the present while incorporating a model of uncertainty about future events (scenarios). These problems present serious computational difficulties as the number of scenarios becomes large and the complexity of the system and planning horizons increase, necessitating the use of parallel computing. Our novel hybrid parallel implementation PIPS is based on interior-point methods and uses a Schur complement technique to obtain a scenario-based decomposition of the linear algebra. PIPS is applied to a stochastic economic dispatch problem that uses hourly wind forecasts and a detailed physical power flow model. Solving this problem is necessary for efficient integration of wind power with the Illinois power grid and real-time energy market. Strong scaling efficiency of 96% is obtained on 32 racks (131,072 cores) of the "Intrepid" Blue Gene/P system at Argonne National Laboratory.