Gradient Methods and Software


  • Software

  • William W. Hager and Hongchao Zhang, An Active Set Algorithm for Nonlinear Optimization with Polyhedral Constraints, Science China Mathematics, ICIAM Special Issue, 59 (2016), pp. 1525-1542, doi: 10.1007/s11425-016-0300-6

  • William W. Hager and Hongchao Zhang, Projection onto a Polyhedron that Exploits Sparsity, SIAM Journal on Optimization, 29 (2016), 1773-1798, doi:10.1137/15M102825X

  • William W. Hager and Hongchao Zhang, Projection onto a Polyhedron that Exploits Sparsity, paper plus data.

  • Timothy A. Davis, William W. Hager, and James T. Hungerford, An Efficient Hybrid Algorithm for the Separable Convex Quadratic Knapsack Problem, ACM TOMS, 42 (2016), pp. 1-25.

  • William W. Hager and Hongchao Zhang, The Limited Memory Conjugate Gradient Method, SIAM Journal on Optimization, 23 (2013), pp. 2150-2168.
  • Performance data for CG_DESCENT 6.0.

  • William W. Hager and Hongchao Zhang, An Affine Scaling Method for Optimization Problems with Polyhedral Constraints, Computational Optimization and Application, 59 (2014), pp. 163-183, DOI 10.1007/s10589-013-9535-x

  • Maria D. Gonzalez-Lima, William W. Hager, and Hongchao Zhang, An Affine-scaling Interior-point Method for Continuous Knapsack Constraints with Application to Support Vector Machines, SIAM Journal on Optimization, 21 (2011), pp. 361-390.

  • W. W. Hager, B. A. Mair, and H. Zhang, An Affine-scaling Interior-point CBB Method for Box-Constrained Optimization, Mathematical Programming, 119 (2009), pp. 1-32.

  • W. W. Hager and H. Zhang, A new conjugate gradient method with guaranteed descent and an efficient line search, SIAM Journal on Optimization, 16 (2005), 170-192.
  • Performance data for SIOPT paper.

  • W. W. Hager and H. Zhang, Algorithm 851: CG_DESCENT, A conjugate gradient method with guaranteed descent, ACM Transactions on Mathematical Software, 32 (2006), 113-137.
  • Performance data for ACM TOMS paper.

  • W. W. Hager and H. Zhang, A survey of nonlinear conjugate gradient methods, Pacific Journal of Optimization, 2 (2006), pp. 35-58.

  • Y-H. Dai, W. W. Hager, K. Schittkowski, and H. Zhang, The cyclic Barzilai-Borwein method for unconstrained optimization, IMA Journal on Numerical Analysis, 26 (2006), pp. 604 - 627.

  • W. W. Hager and H. Zhang, A new active set algorithm for box constrained optimization, SIAM Journal on Optimization, 17 (2006), pp. 526-557.
  • Performance data for active set paper.
  • W. W. Hager and H. Zhang, Recent advances in bound constrained optimization, in System Modeling and Optimization, F. Ceragioli, A. Dontchev, H. Furuta, K. Marti, and L. Pandolfi, eds., Springer, 2006, pp. 67-82. (22nd IFIP TC 7 Conference on System Modeling and Optimization, Turin, Italy, July 18-22, 2005).

  • H. Zhang and W. W. Hager, A nonmonotone line search technique and its application to unconstrained optimization, SIAM Journal on Optimization, 14 (2004), pp. 1043-1056.
  • W. W. Hager and S. C. Park, The gradient projection method with exact line search, Journal of Global Optimization, 30 (2004), pp. 103-118.

  • W. W. Hager, Analysis and implementation of a dual algorithm for constrained optimization, Journal of Optimization Theory and Applications, 79 (1993), pp. 427-462.

  • W. W. Hager, A derivative-based bracketing scheme for univariate minimization and the conjugate gradient method, Computers Math. Applic., 18 (1989), pp. 779-795.

  • N. Ghosh and W. W. Hager, A derivative-free bracketing scheme for univariate minimization, Computers Math. Applic., 20 (1990), pp. 23-34.

  • Holly Peters Hirst, N-step quadratic convergence in the conjugate gradient method (Phd thesis at Penn State University, 1989)

  • GNU GENERAL PUBLIC LICENSE