Software

Software by Professor M. J. D. Powell

Professor M. J. D. Powell kindly authorizes me to provide his software on this page. If you have problems in downloading, please feel free to contact me. For more information on the code, please contact Professor Powell (mjdp [&] cam.ac.uk).

  • COBYLA (Constrained Optimization BY Linear Approximations), an algorithm that seeks the least value of a nonlinear function subject to nonlinear inequality constraints, without using derivatives of the objective function or the constraints. Implemented in fortran 77 (single precision only). Released on May 7, 1992. [paper] [wikipedia]

  • NEWUOA, an algorithm that solves unconstrained optimization problems without using derivatives. Developed from UOBYQA (Unconstrained Optimization BY Quadratic Approximation, Powell, 2000). Implemented in fortran 77. Released on Dec. 16, 2004. [paper] [wikipedia]

  • BOBYQA (Bound Optimization BY Quadratic Approximation), an algorithm that seeks the least value of a nonlinear function subject to bound constraints, without using derivatives of the objective function. Implemented in fortran 77. Released on Jan. 5, 2009. [paper] [wikipedia]

  • LINCOA (LINearly Constrained Optimization Algorithm), an algorithm that seeks the least value of a nonlinear function subject to linear inequality constraints, without using derivatives of the objective function. Implemented in fortran 77. Released on Dec. 6, 2013. [paper] [wikipedia]

Subroutines by myself

Here are some subroutines by me. They are written in the hope that they will be helpful, but there is no guarantee that they will work properly. They probably call some subroutines that are not provided here. In that case I try to instruct in the comments how to obtain those subroutines.

Optimization

  • A fortran subroutine to seek an inexact solution to a trust region subproblem

 begin{array}{rl}     min&frac{1}{2} d^top B d + g^top d     textnormal{s.t.}&|d| le Delta. end{array}
  • A fortran subroutine to seek an inexact solution to a trust region subproblem with box constrains, namely

 begin{array}{rl}     min&frac{1}{2} d^top B d + g^top d     textnormal{s.t.}&|d| le Delta,                      & lle dle u. end{array}

Numerical linear algebra

  • A fortran subroutine to solve a linear system with a positive definite coefficient matrix.

  • A fortran subroutine to calculate all the eigenvalues of a symmetric matrix.

  • A fortran subroutine to calculate the largest k eigenvalues of a symmetric matrix and the corresponding eigenvectors.