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 43 articles )

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  1. Kopaničáková, Alena; Krause, Rolf: A recursive multilevel trust region method with application to fully monolithic phase-field models of brittle fracture (2020)
  2. Scheufele, Klaudius; Subramanian, Shashank; Mang, Andreas; Biros, George; Mehl, Miriam: Image-driven biophysical tumor growth model calibration (2020)
  3. Larson, Jeffrey; Menickelly, Matt; Wild, Stefan M.: Derivative-free optimization methods (2019)
  4. Mang, Andreas; Gholami, Amir; Davatzikos, Christos; Biros, George: CLAIRE: a distributed-memory solver for constrained large deformation diffeomorphic image registration (2019)
  5. Scheufele, Klaudius; Mang, Andreas; Gholami, Amir; Davatzikos, Christos; Biros, George; Mehl, Miriam: Coupling brain-tumor biophysical models and diffeomorphic image registration (2019)
  6. 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)
  7. C. Cartis; L. Roberts: A Derivative-Free Gauss-Newton Method (2017) arXiv
  8. Chang, J.; Karra, S.; Nakshatrala, K. B.: Large-scale optimization-based non-negative computational framework for diffusion equations: parallel implementation and performance studies (2017)
  9. Chang, J.; Nakshatrala, K. B.: Variational inequality approach to enforcing the non-negative constraint for advection-diffusion equations (2017)
  10. 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)
  11. 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)
  12. Nakshatrala, K. B.; Nagarajan, H.; Shabouei, M.: A numerical methodology for enforcing maximum principles and the non-negative constraint for transient diffusion equations (2016)
  13. Eisenhauer, Philipp; Heckman, James J.; Mosso, Stefano: Estimation of dynamic discrete choice models by maximum likelihood and the simulated method of moments (2015)
  14. León Baldelli, A. A.; Babadjian, J.-F.; Bourdin, B.; Henao, D.; Maurini, C.: A variational model for fracture and debonding of thin films under in-plane loadings (2014)
  15. Michel-Griesser, Laurent; Picasso, Marco; Farinotti, Daniel; Funk, Martin; Blatter, Heinz: Bedrock topography reconstruction of glaciers from surface topography and mass-balance data (2014)
  16. Zeng, X.; Anitescu, M.: Sequential Monte Carlo sampling in hidden Markov models of nonlinear dynamical systems (2014)
  17. Heyn, Toby; Anitescu, Mihai; Tasora, Alessandro; Negrut, Dan: Using Krylov subspace and spectral methods for solving complementarity problems in many-body contact dynamics simulation (2013)
  18. Raim, Andrew M.; Gobbert, Matthias K.; Neerchal, Nagaraj K.; Morel, Jorge G.: Maximum-likelihood estimation of the random-clumped multinomial model as a prototype problem for large-scale statistical computing (2013)
  19. Jhurani, Chetan; Demkowicz, Leszek: Multiscale modeling using goal-oriented adaptivity and numerical homogenization. I: Mathematical formulation and numerical results (2012)
  20. Kalenkova, A. A.: An algorithm of automatic workflow optimization (2012)

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