Gradient Methods and Software


  • Software Archive

  • Source code for BLG Version 1.1, November 16, 2010 (solve problems with bound and linear constraints using gradient methods: gradient projection, affine scaling, or Frank-Wolfe).
  • Source code for SVMsubspace Version 1.0, September 30, 2010 (solve Support Vector Machine problems by subspace methods and BLG)

  • Maria D. Gonzalez-Lima, W. W. Hager, and H. 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.

  • Source code for ASL Version 1.2, September 9, 2009 (affine scaling method, linear constraint, bound constraints)
  • Source code for SSM Version 1.1, September 25, 2009 (sequential subspace method for sphere constrained optimization)
  • Source code for ASA_CG Version 2.2, April 14, 2011 (bound constrained optimization)
  • Source code for CG_DESCENT Version 5.3 , May 18, 2012 (unconstrained optimization) New: function and gradient can be coded in MATLAB

  • 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.
  • Test problem 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.
  • Test problem data for ACM TOMS paper.

  • CG_DESCENT Version 1.4, User's Guide, Novermber 14, 2005

  • 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.
  • Test problem 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.

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

  • GNU GENERAL PUBLIC LICENSE