A case study in the performance and scalability of optimization algorithms. We analyze the performance and scalabilty of algorithms for the solution of large optimization problems on high-performance parallel architectures. Our case study uses the GPCG (gradient projection, conjugate gradient) algorithm for solving bound-constrained convex quadratic problems. Our implementation of the GPCG algorithm within the Toolkit for Advanced Optimization (TAO) is available for a wide range of high-performance architectures and has been tested on problems with over 2.5 million variables. We analyze the performance as a function of the number of variables, the number of free variables, and the preconditioner. In addition, we discuss how the software design facilitates algorithmic comparisons.

References in zbMATH (referenced in 53 articles )

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  1. Scherer, Jean-Michel; Brach, Stella; Bleyer, Jérémy: An assessment of anisotropic phase-field models of brittle fracture (2022)
  2. Vogt, Ryan H.; Leyffer, Sven; Munson, Todd S.: A mixed-integer PDE-constrained optimization formulation for electromagnetic cloaking (2022)
  3. Zhang, Hong; Constantinescu, Emil M.; Smith, Barry F.: \textttPETScTSAdjoint: a discrete adjoint ODE solver for first-order and second-order sensitivity analysis (2022)
  4. Leyffer, Sven; Manns, Paul; Winckler, Malte: Convergence of sum-up rounding schemes for cloaking problems governed by the Helmholtz equation (2021)
  5. Malte Brunn, Naveen Himthani, George Biros, Miriam Mehl, Andreas Mang: CLAIRE: Constrained Large Deformation Diffeomorphic Image Registration on Parallel Computing Architectures (2021) not zbMATH
  6. Bleyer, Jeremy: Automating the formulation and resolution of convex variational problems. Applications from image processing to computational mechanics (2020)
  7. Kopaničáková, Alena; Krause, Rolf: A recursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture (2020)
  8. Scheufele, Klaudius; Subramanian, Shashank; Mang, Andreas; Biros, George; Mehl, Miriam: Image-driven biophysical tumor growth model calibration (2020)
  9. Larson, Jeffrey; Menickelly, Matt; Wild, Stefan M.: Derivative-free optimization methods (2019)
  10. Mang, Andreas; Gholami, Amir; Davatzikos, Christos; Biros, George: CLAIRE: a distributed-memory solver for constrained large deformation diffeomorphic image registration (2019)
  11. Phlipot, Gregory P.; Kochmann, Dennis M.: A quasicontinuum theory for the nonlinear mechanical response of general periodic truss lattices (2019)
  12. Scheufele, Klaudius; Mang, Andreas; Gholami, Amir; Davatzikos, Christos; Biros, George; Mehl, Miriam: Coupling brain-tumor biophysical models and diffeomorphic image registration (2019)
  13. Yang, Haijian; Sun, Shuyu; Li, Yiteng; Yang, Chao: A fully implicit constraint-preserving simulator for the black oil model of petroleum reservoirs (2019)
  14. Mang, Andreas; Gholami, Amir; Davatzikos, Christos; Biros, George: PDE-constrained optimization in medical image analysis (2018)
  15. Bobenko, Alexander I.; Dimitrov, Nikolay; Sechelmann, Stefan: Discrete uniformization of polyhedral surfaces with non-positive curvature and branched covers over the sphere via hyper-ideal circle patterns (2017)
  16. C. Cartis; L. Roberts: A Derivative-Free Gauss-Newton Method (2017) arXiv
  17. Chang, J.; Karra, S.; Nakshatrala, K. B.: Large-scale optimization-based non-negative computational framework for diffusion equations: parallel implementation and performance studies (2017)
  18. Chang, J.; Nakshatrala, K. B.: Variational inequality approach to enforcing the non-negative constraint for advection-diffusion equations (2017)
  19. Vašatová, Alena; Tomčala, Jiří; Sojka, Radim; Pecha, Marek; Kružík, Jakub; Horák, David; Hapla, Václav; Čermák, Martin: Parallel strategies for solving the FETI coarse problem in the PERMON toolbox. (2017)
  20. Arreckx, Sylvain; Lambe, Andrew; Martins, Joaquim R. R. A.; Orban, Dominique: A matrix-free augmented Lagrangian algorithm with application to large-scale structural design optimization (2016)

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Further publications can be found at: http://www.mcs.anl.gov/research/projects/tao/publications/index.html