- Numerical optimization
- Stochastic programming and optimization of energy systems in the presence of uncertainty
- Parallel linear algebra
- High performance computing
- Co-PI, Optimization of Complex Energy System Under Uncertainty, DOE Incite Award 2012-2013, 10 million core hours (2012). PI: Mihai Anitescu.
- C. G. Petra, B. Gavrea, M. Anitescu, F. A. Potra. A computational study on the use of an optimization based method in the simulation of large multi-body systems. Optimization Methods and Software, Volume 24, Issue 6, Pages 871-894, 2009.
- S. Al-Homidan, M. M. Alshahrani, C. G. Petra, F. A. Potra. Minimal Condition Number for Positive Definite Hankel Matrices using Semidefinite Programming. Linear Algebra and Its Applications, Volume 433, Issue 6, Pages 1101-1109, November 2010.
- F. Gurtuna, C. G. Petra, F. A. Potra, O. Schevchenko, A. Vancea. Corrector-Predictor Methods for sufficient linear complementarity problems. Computational Optimization and Applications, Volume 48, Issue 3, Pages 453-485, April 2011.
- A. Draganescu, C. G. Petra. Multigrid preconditioning of linear systems for
interior point methods applied to a class of bound-constrained control problems.
SIAM Journal on Numerical Analysis, Volume 50, Number 1, Pages 328-353, 2012.
- C. G. Petra, M. Anitescu. A preconditioning technique for Schur complement systems arising in stochastic optimization. Computational Optimization and Applications, Pages 315-344, Volume 52, Issue 2, 2012.
- M. Lubin, C. G. Petra, M. Anitescu. On the parallel solution of dense saddle-point linear systems arising in stochastic programming. Optimization Methods and Software, Volume 27, Number 4-5, Pages 845-864, 2012.
- M. Lubin, C. G. Petra, M. Anitescu, and V. Zavala. Scalable Stochastic Optimization of Complex Energy Systems. In Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis (SC '11), pages 64:1-64:10. ANL preprint.
- M. Anitescu, C. G. Petra. Higher-Order Confidence Intervals for Stochastic Programming using Bootstrapping. In review - Mathematical Programming, ANL preprint.
- M. Lubin, J. A. J. Hall, C. G. Petra, and M. Anitescu. Parallel distributed-memory simplex for large-scale stochastic LP problems., Computational Optimization and Applications, 2013, DOI , ANL preprint.
- M. Lubin, K. Martin, C.G. Petra, and Burhaneddin Sandikic. On parallelizing dual decomposition in stochastic integer programming. Operations Research Letters 41(3), pages 252-258, 2013, DOI , ANL preprint.
- C. G. Petra, Olaf Schenk, Miles Lubin, Klaus Gaertner. An augmented incomplete factorization approach for computing the Schur complement in stochastic optimization. Submitted to SIAM Journal on Scientific Computing (SISC), ANL preprint.
- C. G. Petra, O. Schenk, M. Anitescu. Real-time Stochastic Optimization of Complex Energy Systems on High Performance Computers. To be submitted. ANL preprint.
- R. Serban, C. Petra. User Documentation for IDAS v1.0.0, 2008, Report UCRL-SM-234051, Lawrence Livermore National Laboratory.
- Scalable Stochastic Programming, DOE Applied Math Meeting (2010)
- Scalable Stochastic Programming, Informs Annual Meeting (2010)
- Scalable Stochastic Programming, Informs Computing Society (2011)
- Scalable Stochastic Programming, AMS Southeastern (2011)
- Scalable Stochastic Programming, Informs Annual Meeting (2011)
- Higher-order Confidence Intervals for Stochastic Programming using Bootstrapping, Informs Annual Meeting (2012)
- On Parallelizing Dual Decomposition in Stochastic Integer Programming, Informs Annual Meeting (2012)
- Stochastic optimization of complex energy systems on high-performance computers, Informs Annual Meeting (2012), Informs Computing Society (2013), SIAM CSE (2013)