Publications

  1. "Optimization Methods for Large-Scale Machine Learning"
    L. Bottou, F. Curtis and J. Nocedal
    Under Review (2016).
    Abstract | Download (pdf) | Errata (pdf)
  2. "On Large-Batch Training for Deep Learning: Generalization Gap and Sharp Minima"
    N. Keskar, D. Mudigere, J. Nocedal, M. Smelyanskiy, P. Tang
    International Conference on Learning Representations (ICLR, 2017).
    Download (pdf)
  3. "A Multi-Batch L-BFGS Method for Machine Learning"
    A. Berahas, J. Nocedal and M. Takac
    Advances in Neural Information Processing Systems (NIPS, 2016).
    Download (pdf)
  4. "A Second-Order Method for Convex L1-Regularized Optimization with Active Set Prediction"
    N. Keskar, J. Nocedal, F. Oztoprak and A. Waechter
    Optimization Methods and Software (2016).
    Abstract | Download (pdf)
  5. "A Stochastic Quasi-Newton Method for Large-Scale Optimization"
    R. Byrd, S. Hansen, J. Nocedal and Y. Singer
    SIAM Journal on Optimization (2016).
    Abstract | Download (pdf)
  6. "An Algorithm for Quadratic l1-Regularized Optimization with a Flexible Active-Set Strategy"
    R. Byrd, J. Nocedal and S. Solntsev
    To appear in Optimization Methods and Software (2015).
    Abstract | Arxiv | Code
  7. "An Inexact Successive Quadratic Approximation method for l1-Regularized Optimization"
    R. Byrd, J. Nocedal and F. Oztoprak
    Mathematical Programming B (2015).
    Abstract | Download (pdf)
  8. "An Interior Point Method for Nonlinear Programming with Infeasibility Detection Capabilities"
    J. Nocedal, F. Oztoprak and R.A. Waltz
    Optimization Methods and Software, Vol 29, Issue 4 (2014).
    Abstract | Download (pdf)
  9. "Subspace accelerated matrix splitting algorithms for bound-constrained quadratic programming and linear complementarity problems"
    D. Robinson, L. Feng, J. Nocedal and J.S. Pang
    SIAM Journal on Optimization (2013).
    Abstract | Download (pdf)
  10. "On the Use of Piecewise Linear Models in Nonlinear Programming"
    R. Byrd, J. Nocedal, R. Waltz and Y.Wu
    Mathematical Programming Volume 137, Issue 1 (2013), Page 289-324
    Abstract | Download (pdf)
  11. "Second Order Methods for Optimizing Convex Matrix Functions and Sparse Covariance Clustering"
    G. Chin, J. Nocedal, P.A. Olsen, S.J. Rennie
    IEEE Transactions on Audio, Speech, and Language Processing (2013).
    Abstract | Download (pdf)
  12. "Sample Size Selection in Optimization Methods for Machine Learning"
    R. Byrd, G. Chin, J. Nocedal and Y. Wu
    Mathematical Programming B (2012).
    Abstract | Download (pdf)
  13. "A family of second-order methods for convex l1-regularized optimization"
    R. Byrd, G. Chin, J. Nocedal, F. Oztoprak
    Mathematical Programming A (2015).
    Abstract | Download (pdf)
  14. "A Line Search Exact Penalty Method Using Steering Rules"
    R. Byrd, G. Lopez-Calva, J. Nocedal
    Mathematical Programming 133,1, pp. 39-73 (2012).
    Abstract | BibTex | Download (pdf)
  15. "Second-order methods for L1 regularized problems in machine learning"
    S. Hansen and J. Nocedal
    IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP) (2012).
    Abstract | Download (pdf)
  16. "Newton-like methods for sparse inverse covariance estimation"
    F. Oztoprak, J. Nocedal, S. Rennie, P. Olsen
    Advances in Neural Information Processing Systems (NIPS) (2012).
    Abstract | Download (pdf)
  17. "On the Solution of Complementarity Problems Arising in American Options Pricing"
    L. Feng, V. Linetsky, J.L. Morales, J. Nocedal
    to appear in Optimization Methods and Software (2011).
    Abstract | Download (pdf)
  18. "On the Use of Stochastic Hessian Information in Optimization Methods for Machine Learning"
    R. Byrd, G. Chin and W. Neveitt, J. Nocedal
    SIAM J. on Optimization, vol 21, issue 3, pages 977-995 (2011).
    Abstract | Download (pdf)
  19. "A Sequential Quadratic Programming Algorithm with an Additional Equality Constrained Phase"
    J.L. Morales, J. Nocedal, Y. Wu
    to appear in IMA Journal on Numerical Analysis (2011).
    Abstract | BibTex | Download (pdf)
  20. "Infeasibility Detection and SQP Methods for Nonlinear Optimization"
    R. Byrd, F. Curtis, J. Nocedal
    SIAM J. Optimization, Vol 20, no. 5, (2010).
    Abstract | BibTex | Download (pdf)
  21. "A Matrix-Free Algorithm for Equality Constrained Optimization Problems with Rank-Deficient Jacobians"
    F. Curtis, J. Nocedal, A. Waechter
    SIAM J. Optimization, Vol 20, Issue 3, pp. 1224-1249, (2009).
    Abstract | BibTex | Download (pdf)
  22. "On the Geometry Phase in Model-Based Algorithms for Derivative-Free Optimization"
    G. Fasano, J.L. Morales, J. Nocedal.
    Optimization Methods and Software, Volume 24, Issue 1, February 2009, pp. 145-154 (2009)
    Abstract | Download (pdf)
  23. "An Inexact Newton Method for Nonconvex Equality Constrained Optimization"
    R. Byrd, F. Curtis, J. Nocedal.
    Mathematical Programming vol 122, Issue 2, pp. 273-299,(2009).
    Abstract | BibTex | Download (pdf)
  24. "An Algorithm for the Fast Solution of Linear Complementarity Problems"
    J.L. Morales, J. Nocedal, M. Smelyanskiy.
    Numerische Mathematik, DOI: 10.1007/s00211-008-0183-5 (2008)
    Abstract | BibTex | Download (pdf)
  25. "Flexible Penalty Functions for Nonlinear Constrained Optimization"
    F. Curtis, J. Nocedal
    IMA Journal on Numerical Analysis  (2008).
    Abstract | BibTex | Download (pdf)
  26. "Data Assimilation in Weather Forecasting: A Case Study in PDE-Constrained Optimization"
    M. Fisher, J. Nocedal, Y. Tremolet, S. Wright
    Optimization and Engineering , DOI: 10.1007/s11081-008-9051-5 (2009).
    Abstract | BibTex | Download (pdf)
  27. "Inexact SQP Methods for Equality Constrained Optimization"
    R. Byrd, F. Curtis, J. Nocedal.
    SIAM J. Optimization, Vol. 19, No. 1, pp. 351-369 (2008)
    Abstract | BibTex | Download (pdf)
  28. "A Numerical Study of Active-Set and Interior-Point Methods for Bound Constrained Optimization"
    L. Hei, J. Nocedal, R. Waltz
    “Modeling, Simulation and Optimization of Complex Processes”,
    editors Bock H. G., Kostina E. A., Phu H. X., Rannacher R. (2008) Springer.
    Abstract | BibTex | Download (pdf)
  29. "Steplength Selection in Interior-Point Methods"
    F. Curtis, J. Nocedal
    Applied Math Letters, Volume 20, Issue 5, Pages 516-523 (2007).
    Abstract | Download (pdf)
  30. "KNITRO: An Integrated Package for Nonlinear Optimization"
    R. Byrd, J. Nocedal, R. Waltz.
    “Large-Scale Nonlinear Optimization”,
    eds.: G. Di Pillo, M. Roma, pp.35-60 Springer (2006)
    Abstract | BibTex | Download (pdf)
  31. "Interior Point Methods for Mathematical Programs with Complementarity Constraints"
    G. Lopez-Calva, S. Leyffer, J. Nocedal.
    SIAM J. Optimization, Vol. 17, No. 1, pp: 52-77 (2006).
    Abstract | BibTex | Download (pdf)
  32. "Adaptive Barrier Update Strategies for Nonlinear Interior Methods"
    J. Nocedal, A. Waechter, R. Waltz
    SIAM J. Optimization, Volume 19, Issue 4, pp. 1674-1693 (2009)
    Abstract | BibTex | Download (pdf)
  33. "Steering Exact Penalty Methods for Nonlinear Programming"
    R. Byrd, J. Nocedal, R. Waltz.
    Optimization Methods and Software, Vol. 23, No. 2, pp. 197-213 (2008).
    Abstract | BibTex | Download (pdf)
  34. "An Interior Algorithm for Nonlinear Optimization that Combines Line Search and Trust Region Steps"
    J.L. Morales, J. Nocedal, D. Orban, R. Waltz.
    Mathematical Programming A, Vol. 102, pp. 391-408 (2006).
    Abstract | Download (pdf)
  35. "On the Convergence of Successive Linear Programming Algorithms"
    R. Byrd, N. Gould, J. Nocedal, R. Waltz.
    SIAM J. Optimization, Vol. 16, No. 2, pp.471-489 (2005).
    Abstract | BibTex | Download (pdf)
  36. "A Starting-Point Strategy for Nonlinear Interior Methods,"
    M. Gertz, J. Nocedal, A. Sartenaer.
    Applied Math Letters, Vol 17, pp. 945-952 (2004).
    Abstract | BibTex | Download (pdf) 
  37. "An Active-Set Algorithm for Nonlinear Programming Using Linear Programming and Equality Constrained Subproblems"
    R. Byrd, N. Gould, J. Nocedal, R. Waltz.
    Mathematical Programming B, Vol. 100, No. 1, pp. 27-48 (2004).
    Abstract | BibTex | Download (pdf)
  38. "On the Convergence of Newton Iterations to Non-Stationary Points"
    R. Byrd, M. Marazzi, J. Nocedal.
    Mathematical Programming A, Vol. 99, pp. 127-148 (2004).
    Abstract | BibTex | Download (pdf)
  39. "Assessing the Potential of Interior Methods for Nonlinear Optimization"
    J.L. Morales, J.P. Goux, G. Liu, J. Nocedal, R. Waltz.
    Lecture Notes in Computational Science and Engineering,
    edited by L. T. Biegler, O. Ghattas, M. Heinkenschloss, B. van Bloemen
    Vol. 30, pp. 167-183 Springer Verlag (2003).
    Abstract | Download (pdf) 
  40. "Feasible Interior Methods Using Slacks for Nonlinear Optimization"
    R. Byrd, J. Nocedal, R. Waltz.
    Computational Optimization and Applications, Vol 26, No. 1 (2003)
    Abstract | BibTex | Download (pdf)
  41. "Wedge trust region methods for derivative free optimization"
    M. Marazzi, J. Nocedal
    Mathematical Programming, Vol. 91 No. 2, pp.289-30 (2002)
    Abstract | BibTex | Download (pdf) 
  42. "iNEOS: An Interactive Environment for Nonlinear Optimization"
    M. Good, J.P. Goux, J. Nocedal, V. Pereyra.
    Applied Numerical Mathematics, Vol. 40: pp.49-58 (January 2002)
    Abstract | BibTex | Download (pdf)   
  43. "An Enriched Algorithm for Large-Scale Nonlinear Optimization"
    J.L. Morales, J. Nocedal.
    Computational Optimization and Applications (COAP), Vol. 21, No. 2, pp. 143-154, (February 2002)
    Abstract | Download (pdf) 
  44. "Feasibility Control in Nonlinear Optimization "
    M. Marazzi, J. Nocedal
    ''Foundations of Computational Mathematics'', eds. A DeVore, A. Iserles, E. Suli
    London Mathematical Society Lecture Notes; Series 284, pp. 125-154,
    Cambridge University Press (2001)
    Abstract | BibTex | Download (pdf)
  45. "Algorithm PREQN: FORTRAN subroutines for preconditioning the conjugate gradient method "
    J.L. Morales, J. Nocedal
    ACM Transactions on Mathematical Software. Vol. 27, No. 1, pp.83-91 (2001)
    Abstract | BibTex | Download (pdf) >
  46. "Numerical Experience with a Reduced Hessian Method for Large-Scale Constrained Optimization"
    L. Biegler, J. Nocedal, C. Schmid, D. Ternet.
    Computational Optimization and Applications, Vol. 15, No. 1 (2000)
    Abstract | BibTex | Download (pdf) 
  47. "Automatic Preconditioning by Limited Memory Quasi-Newton Updating"
    J.L. Morales, J. Nocedal.
    SIAM J. Optimization, Vol. 10, No. 4, pp. 1079-1096 (2000)
    Abstract | BibTex | Download (pdf) 
  48. "A Trust Region Method Based on Interior Point Techniques for Nonlinear Programming "
    R. Byrd, J.C. Gilbert, J. Nocedal.
    Mathematical Programming A, Vol. 89: pp. 149-185 (2000)
    Abstract | BibTex | Download (pdf) 
  49. "On the Behavior of the Gradient Norm in the Steepest Descent Method "
    J. Nocedal, A. Sartenaer, C. Zhu
    Computational Optimization and Applications (May 2000).
    Abstract | Download (pdf) 
  50. "On the solution of equality constrained quadratic programming problems arising in optimization "
    N.I.M. Gould, M.E. Hribar, J. Nocedal.
    SIAM J. Sci. Computing, Vol 23, No.4, pp. 1375-1394 (2001)
    Abstract | BibTex | Download (pdf) 
  51. "An Interior Point Algorithm for Large Scale Nonlinear Programming "
    R.H. Byrd, M.E. Hribar, J. Nocedal
    SIAM J. Optimization, 9,4, pp.877-900 (1999)
    Abstract | BibTex | Download (pdf) 
  52. "Combining trust region and line search techniques"
    J. Nocedal, Y. Yuan.
    Advances in Nonlinear Programming, ed. Y. Yuan, pp. 153-175 (1998) Kluwer
    Abstract | BibTex | Download (pdf) 
  53. "On the modified absolute-value factorization norm for trust-region minimization"
    N.I.M. Gould, J. Nocedal.
    High Performance Algorithms and Software in Nonlinear Optimization, pp. 225-241,
    eds. R. De Leone, A. Murli, P. M. Pardalos, G. Toraldo (1998) Kluwer
    Abstract | BibTex | Download (pdf) 
  54. "On the Implementation of an Algorithm for Large-Scale Equality Constrained Optimization"
    M. Lalee, J. Nocedal, T. Plantenga
    SIAM Journal on Optimization Vol. 8, No. 3, pp. 682-706. (1998)
    Abstract | BibTex | Download (pdf) 
  55. "On the Local Behavior of an Interior Point Method for Nonlinear Programming"
    R. Byrd, G. Liu, J. Nocedal
    Numerical Analysis , eds. D.F. Griffiths and D.J. Higham, pp.37-56 (1997) Addison Wesley Longman
    Abstract | BibTex | Download (pdf) 
  56. "Large Scale Unconstrained Optimization "
    J. Nocedal
    The State of the Art in Numerical Analysis, pp. 311-338,
    eds: A. Watson and I. Duff, (1997) Oxford University Press.
    Abstract | Download (pdf) 
  57. "Algorithm 778: L-BFGS-B, FORTRAN routines for large scale bound constrained optimization"
    R. Byrd, P. Lu, J. Nocedal, C. Zhu.
    ACM Transactions on Mathematical Software, Vol 23, No. 4, pp. 550 - 560 (1997)
    Abstract | BibTex | Download (pdf)
  58. "Towards a Discrete Newton Method with Memory for Large-Scale Optimization"
    R. Byrd, J. Nocedal, C. Zhu.
    Nonlinear Optimization and Applications, edited by G. Di Pillo, F. Giannessi (1996) Plenum
    Abstract | Download (pdf) 
  59. "A Limited Memory Algorithm for Bound Constrained Optimization"
    R.H. Byrd, P. Lu, J. Nocedal.
    SIAM Journal on Scientific and Statistical Computing , Vol. 16, No. 5, pp. 1190-1208 (1995)
    Abstract | Download (pdf) 
  60. "A Reduced Hessian Method for Large Scale Constrained Optimization"
    L. Biegler, J. Nocedal, C. Schmid.
    SIAM Journal on Optimization , Vol. 5, No. 2, pp.314-347 (1995)
    Abstract | BibTex | Download (pdf) 
  61. "Representations of Quasi-Newton Matrices and their use in Limited Memory Methods"
    R. Byrd, J. Nocedal, R. Schnabel.
    Mathematical Programming, Vol. 63, No. 4, pp. 129-156 (1994)
    Abstract | Download (pdf) 
  62. "Theory of Algorithms for Unconstrained Optimization"
    J. Nocedal
    Acta Numerica Vol. 1, pp. 199-242 (1992)
    Abstract | Download (pdf) 
  63. "On the Limited Memory Method for Large Scale Optimization"
    D.C. Liu, J. Nocedal.
    Mathematical Programming B , Vol. 45, No. 3, pp. 503-528 (1989)
    Abstract | Download (pdf)