Cosmin Gheorghita Petra

Portrait of  Cosmin Gheorghita Petra

  • Title
    Computational Mathematician
  • Email
    petra1@llnl.gov
  • Phone
    (925) 424-6261
  • Organization
    Not Available

Cosmin G. Petra is a computational mathematician in the Center for Applied Scientific Computing at Lawrence Livermore National Laboratory. Cosmin's work focuses on high-performance computing algorithms and C/C++ solvers for mathematical optimization with emphasis on applications in complex energy systems.

Prior to joining the Center for Applied Scientific Computing, Cosmin was with Argonne National Laboratory as a computational mathematician and, prior to that, hold software engineer/numerical analyst positions in IT industry. Cosmin obtained an M.S. and a Ph.D. in Applied Mathematics from the University of Maryland, Baltimore County, in 2006 and 2009, respectively.

Research appointments

  • 2016-present - Computer Scientist/Computational Mathematician, Center for Applied Scientific Computing, Lawrence Livermore National Laboratory.
  • 2015-2020 - Adjunct Asst. Professor, School of Natural Sciences, University of California, Merced.
  • 2012-2016 - Asst. Computational Mathematician, MCS Division, Argonne National Laboratory.
  • 2009-2012 - Postdoctoral Appointee, MCS Division, Argonne National Laboratory.

Research interests

  • Scalable algorithms for optimization, control, and design under uncertainty
  • High-performance computing algorithms for mathematical optimization at extreme scale
  • Scientific computing and extreme-scale computing
  • Power grid optimization of real-world large-scale power systems

Recent and ongoing projects

  • Scalable algorithms for optimization, optimal control, and optimal design
  • HPC optimization solver for continuous optimization - HiOp
  • Optimization of power grid systems, mainly, solving real-world AC optimal power flows with contingency analysis

2006-2009 Ph.D. in Applied Mathematics - University of Maryland, Baltimore County, Baltimore, Maryland

2005-2006 M.S. in Applied Mathematics - University of Maryland, Baltimore County, Baltimore, Maryland

1998-2002 B.S. in Mathematics and Computer Science - Universitatea Babes-Bolyai, Cluj-Napoca, Romania

  • I. Aravena, D. K. Molzahn, S. Zhang, C. G. Petra, F. E. Curtis, S. Tu, A. Wachter, E. Wei, E. Wong, A. Gholami, K. Sun, X. Sun, S. T. Elbert, J. T. Holzer, A. Veeramany, Recent developments in security-constrained AC optimal power flow, submitted, 2022.
  • J. Wang, C. G. Petra, A nonsmooth nonconvex optimization algorithm for problems with upper-C2 objective, submitted, 2022. arXiv
  • J. J. Brust, R. F. Marcia, C. G. Petra, M. Saunders, RCR: Reduced Compact Representation for Large-scale Optimization with Linear Equality Constraints, SIAM Journal on Scientific Computing, Volume 44, Issue 1, 2022. DOI
  • C. G. Petra, M. Salazar De Troya, N. Petra, Y. Choi, G. M. Oxberry, D. Tortorelli, On the implementation of a quasi-Newton interior-point method for PDE-constrained optimization using finite element discretizations, accepted to Optimization Methods and Software, 2022.
  • C. G. Petra, I. A. Solis, Solving realistic security-constrained optimal power flow problems, submitted, 2021. arXiv
  • S. Regev, N. Chiang, E. Darve, C. G. Petra, M. A. Saunders, K. Swirydowicz, S. Peles, A Hybrid Direct-Iterative Method for Solving KKT Linear Systems, in review, 2021.
  • J. Wang, N, Chiang, C. G. Petra, An asynchronous distributed-memory optimization solver for two-stage stochastic programming problems, 20th International Symposium on Parallel and Distributed Computing (ISPDC), 2021. DOI
  • J. J. Brust, S. Leyffer, C. G. Petra, Compact Representations of Structured BFGS Matrices, Computational Optimization and Applications, Volume 80, 2021. DOI 
  • R. Vuchkov, C. G. Petra, N. Petra, On the derivation of quasi-Newton formulas for optimization in function spaces, Journal of Numerical Functional Analysis and Optimization, Volume 41, Issue 13, 2020. DOI
  • J. J. Brust, R. F. Marcia, C. G. Petra, Computationally Efficient Decompositions of Oblique Projection Matrices, SIAM Journal on Matrix Analysis and Applications, Volume 41, Issue 2, 2020. DOI
  • E. M. Constantinescu, N. Petra, J. Bessac, C. G. Petra, Statistical Treatment of Inverse Problems Constrained by Differential Equations-Based Models with Stochastic Terms, SIAM Journal on Uncertainty Quantification, Volume 8, Issue 1, 2020. DOI
  • C. G. Petra, N. Chiang, M. Anitescu, A structured quasi-Newton algorithm for optimizing with incomplete Hessian information, SIAM Journal on Optimization, Volume 29, Issue 2, 2019. DOI
  • J. J. Brust, R. F. Marcia, C. G. Petra, Large-scale quasi-Newton trust-region methods with low dimensional linear equality constraints, Journal of Computational Optimization and Applications, Volume 74, Issue 3, 2019. DOI
  • K. Kim, C. G. Petra, V. M. Zavala, An asynchronous bundle-trust-region method for dual decomposition of stochastic mixed-integer programming, SIAM Journal on Optimization, Volume 29, Issue 1, 2019. DOI
  • C. G. Petra, F. Potra, A Homogeneous Model for Monotone Mixed Horizontal Linear Complementarity Problems, Journal of Computational Optimization and Applications, Volume 72, Issue 1, pages 241-267, 2019. DOI
  • V. Rao, K. Kim, M. Schanen, D. A. Maldonado, C. G. Petra, and M. Anitescu, A Multiperiod Optimization-Based Metric of Grid Resilience, Proceedings of the 2019 IEEE PES General Meeting, 2019.
  • C. G. Petra, A memory-distributed quasi-Newton solver for nonlinear programming problems with a small number of general constraints, Journal of Parallel and Distributed Computing, Volume 133, pages 337-348, 2019. DOI
  • M. Schanen, F. Gilbert, C. G. Petra, M. Anitescu, Towards multiperiod AC-based contingency constrained optimal power flow at large scale, “Proceedings to the 20th Power Systems Computation Conference”, 2018. DOI
  • C. G. Petra, F. Qiang, M. Lubin, J. Huchette, On efficient Hessian computation using the edge pushing algorithm in Julia, Optimization Methods and Software, Volume 33(4-6), pages 1010-1029, 2018. DOI
  • N. Petra, C. G. Petra, Z. Zhang, E. M. Constantinescu, and M. Anitescu, A Bayesian Approach for Parameter Estimation with Uncertainty for Dynamic Power Systems, IEEE Transactions on Power Systems, Volume 32(4), pages 2735 - 2743, 2017. DOI.
  • C. G. Petra, V. M. Zavala, E. N. Ruiz, M. Anitescu, A high-performance computing framework for analyzing the economic impacts of wind correlation, Electric Power Systems Research, Volume 141, pages 372-380, 2016. DOI.
  • J. Huchette, M. Lubin, C. G. Petra, Parallel algebraic modeling for stochastic optimization. The First Workshop for High Performance Technical Computing in Dynamic Languages (HPTCDL), Supercomputing 2014. DOI.
  • C. G. Petra, O. Schenk, M. Anitescu. Real-time Stochastic Optimization of Complex Energy Systems on High Performance Computers. Computing in Science & Engineering (CiSE) 16(5), pages 32-42. DOI.
  • N. Chiang, C. G. Petra, V. M. Zavala, Structured Nonconvex Optimization of Large-Scale Energy Systems Using PIPS-NLP. 18th IEEE Power Systems Computations Conference, 2014.
  • C. G. Petra, Olaf Schenk, Miles Lubin, Klaus Gaertner. An augmented incomplete factorization approach for computing the Schur complement in stochastic optimization. SIAM J. Sci. Comput., 36-2, pages C139-C162, 2014. DOI
  • 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
  • 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. DOI
  • 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 55(3), pages 571-596, 2013. Coin-OR INFORMS 2013 Cup winner + 2013 COAP Best Paper. DOI
  • 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.
  • 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.
  • 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.
  • 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. COAP Best Paper 2011 - Honorable mention.
  • 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.

Technical reports

  • S. Peles, K. Perumalla, M. Alam, A. Mancinelli, R. C. Rutherford, J. Ryan, C. G. Petra, Porting the Nonlinear Optimization Library HiOp to Accelerator-Based Hardware Architectures, submitted, 2021.
  • T. Hartland, C. G. Petra, N. Petra, J. Wang, Bound Constrained Partial Differential Equation Inverse Problem Solution by the Semi-Smooth Newton Method, Technical Report LLNL-TR-819385, 2021.
  • C. G. Petra, N. Chiang, J. Wang, "HiOp - User manual", Tech Report LLNL-SM-743591, 2018-2022, Lawrence Livermore National Laboratory.
  • M. Anitescu, C. G. Petra. Higher-Order Confidence Intervals for Stochastic Programming using Bootstrapping, 2012,  Tech Report ANL/MCS-P1964-1011. Argonne National Laboratory.
  • R. Serban, C. G. Petra. User Documentation for IDAS v1.0.0, 2008, Report UCRL-SM-234051, Lawrence Livermore National Laboratory.

Selected talks

  • SC-ACOPF using nonlinear non-convex optimization and high-performance computing, INFORMS Annual Meeting (2019), ARPA-E GridOptimization Outreach Event (2020), Energy Systems and Optimization Workshop - Georgia Tech (2020)
  • Parallel Structured Quasi-Newton Methods for Material Design, SIAM Conference on Optimization (2017), SIAM Student Chapter, UC Davis (2017)
  • Optimization and Design of Complex Engineering Systems using High-Performance Computing, SIAM-CSE (2017).
  • Scalable stochastic optimization of complex energy systems on high-performance computers, Zuse Institut Berlin (2016)
  • Modelling and solving SC-ACOPF problems in parallel, FERC Technical Conference on Increasing Market and Planning Efficiency through Improved Software (2016)
  • Optimization-based parameter estimation of dynamic power grid systems, SIAM UQ (2016).
  • Scalable optimization of complex energy systems using high-performance computing, Joint Mathematics Meeting, SIAM Parallel Processing (2016)
  • Parallel algebraic modelling for stochastic optimization in Julia, Platform for Advanced Scientific Computing Conference (2015)
  • On the role of wind correlation in the economic dispatch of power grid systems, SIAM CSE (2015)