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.

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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. 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)
  5. Zeng, X.; Anitescu, M.: Sequential Monte Carlo sampling in hidden Markov models of nonlinear dynamical systems (2014)
  6. Jhurani, Chetan; Demkowicz, Leszek: Multiscale modeling using goal-oriented adaptivity and numerical homogenization. I: Mathematical formulation and numerical results (2012)
  7. Perez, Ruben E.; Jansen, Peter W.; Martins, Joaquim R.R.A.: PyOpt: a python-based object-oriented framework for nonlinear constrained optimization (2012)
  8. Bauman, Paul T.; Oden, J.Tinsley; Prudhomme, Serge: Adaptive multiscale modeling of polymeric materials with Arlequin coupling and goals algorithms (2009)
  9. 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)
  10. Gondzio, Jacek; Grothey, Andreas: Exploiting structure in parallel implementation of interior point methods for optimization (2009)
  11. Padula, Anthony D.; Scott, Shannon D.; Symes, William W.: A software framework for abstract expression of coordinate-free linear algebra and optimization algorithms (2009)
  12. 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
  13. Friedlander, Michael P.; Leyffer, Sven: Global and finite termination of a two-phase augmented Lagrangian filter method for general quadratic programs (2008)
  14. Gokhale, Nachiket H.; Barbone, Paul E.; Oberai, Assad A.: Solution of the nonlinear elasticity imaging inverse problem: the compressible case (2008)
  15. Tber, Moulay Hicham; El Alaoui Talibi, Mohamed; Ouazar, Driss: Parameters identification in a seawater intrusion model using adjoint sensitive method (2008)
  16. Gondzio, Jacek; Grothey, Andreas: Parallel interior-point solver for structured quadratic programs: Application to financial planning problems (2007)
  17. Benson, Steven J.; Munson, Todd S.: Flexible complementarity solvers for large-scale applications (2006)
  18. McInnes, Lois Curfman; Allan, Benjamin A.; Armstrong, Robert; Benson, Steven J.; Bernholdt, David E.; Dahlgren, Tamara L.; Diachin, Lori Freitag; Krishnan, Manojkumar; Kohl, James A.; Larson, J. Walter; Lefantzi, Sophia; Nieplocha, Jarek; Norris, Boyana; Parker, Steven G.; Ray, Jaideep; Zhou, Shujia: Parallel PDE-based simulations using the common component architecture (2006)
  19. Drummond, L. A.; Marques, O. A.: An overview of the Advanced CompuTational Software (ACTS) collection. (2005)
  20. Kazama, Jun’ichi; Tsujii, Jun’ichi: The use of bigrams to enhance text categorization (2005) ioport

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