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 31 articles )

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  1. 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)
  2. Chang, J.; Karra, S.; Nakshatrala, K.B.: Large-scale optimization-based non-negative computational framework for diffusion equations: parallel implementation and performance studies (2017)
  3. 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)
  4. Nakshatrala, K.B.; Nagarajan, H.; Shabouei, M.: A numerical methodology for enforcing maximum principles and the non-negative constraint for transient diffusion equations (2016)
  5. Eisenhauer, Philipp; Heckman, James J.; Mosso, Stefano: Estimation of dynamic discrete choice models by maximum likelihood and the simulated method of moments (2015)
  6. 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)
  7. Zeng, X.; Anitescu, M.: Sequential Monte Carlo sampling in hidden Markov models of nonlinear dynamical systems (2014)
  8. 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)
  9. Jhurani, Chetan; Demkowicz, Leszek: Multiscale modeling using goal-oriented adaptivity and numerical homogenization. I: Mathematical formulation and numerical results (2012)
  10. Perez, Ruben E.; Jansen, Peter W.; Martins, Joaquim R.R.A.: PyOpt: a python-based object-oriented framework for nonlinear constrained optimization (2012)
  11. Rasch, Arno; Bücker, H.Martin: EFCOSS: an interactive environment facilitating optimal experimental design (2010)
  12. Bauman, Paul T.; Oden, J.Tinsley; Prudhomme, Serge: Adaptive multiscale modeling of polymeric materials with Arlequin coupling and goals algorithms (2009)
  13. Feng, Yusheng; Fuentes, David; Hawkins, Andrea; Bass, Jon M.; Rylander, Marissa Nichole: Optimization and real-time control for laser treatment of heterogeneous soft tissues (2009)
  14. Gondzio, Jacek; Grothey, Andreas: Exploiting structure in parallel implementation of interior point methods for optimization (2009)
  15. Padula, Anthony D.; Scott, Shannon D.; Symes, William W.: A software framework for abstract expression of coordinate-free linear algebra and optimization algorithms (2009)
  16. Feng, Yusheng; Fuentes, David; Hawkins, Andrea; Bass, Jon; Rylander, Marissa Nichole; Elliott, Andrew; Shetty, Anil; Stafford, R.Jason; Oden, J.Tinsley: Nanoshell-mediated laser surgery simulation for prostate cancer treatment (2008) ioport
  17. Friedlander, Michael P.; Leyffer, Sven: Global and finite termination of a two-phase augmented Lagrangian filter method for general quadratic programs (2008)
  18. Gokhale, Nachiket H.; Barbone, Paul E.; Oberai, Assad A.: Solution of the nonlinear elasticity imaging inverse problem: the compressible case (2008)
  19. Tber, Moulay Hicham; El Alaoui Talibi, Mohamed; Ouazar, Driss: Parameters identification in a seawater intrusion model using adjoint sensitive method (2008)
  20. Gondzio, Jacek; Grothey, Andreas: Parallel interior-point solver for structured quadratic programs: Application to financial planning problems (2007)

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