test_nls

test_nls, a FORTRAN90 code which defines test problems for least squares minimization.

The typical problem comprises M functions in N variables, and it is desired to minimize the sum of squares of the values of the functions. Each problem is specified by a starting point, a function and jacobian routines.

The problems include:

  1. Linear function, full rank
  2. Linear function, rank 1.
  3. Linear function, rank 1, zero columns and rows.
  4. Rosenbrock function.
  5. Helical valley function.
  6. Powell singular function.
  7. Freudenstein/Roth function.
  8. Bard function.
  9. Kowalik and Osborne function.
  10. Meyer function.
  11. Watson function.
  12. Box 3-dimensional function.
  13. Jennrich and Sampson function.
  14. Brown and Dennis function.
  15. Chebyquad function.
  16. Brown almost-linear function.
  17. Osborne function 1.
  18. Osborne function 2.
  19. Hanson function 1
  20. Hanson function 2
  21. McKeown function 1
  22. McKeown function 2
  23. McKeown function 3
  24. Devilliers and Glasser function 1
  25. Devilliers and Glasser function 2
  26. Madsen example

Licensing:

The computer code and data files described and made available on this web page are distributed under the MIT license

Languages:

test_nls is available in a FORTRAN90 version.

Related Data and Programs:

DQED, a FORTRAN90 code which seeks the solution of bounded or constrained minimization problems.

MINPACK, a FORTRAN90 code which seeks the solution of nonlinear equations, or the least squares minimization of the residual.

test_nls_test

Reference:

  1. John Dennis, David Gay, and Phuong Vu,
    A new nonlinear equations test problem,
    Technical Report 83-16,
    Mathematical Sciences Department,
    Rice University, (1983 - revised 1985).
  2. N. de Villiers and D. Glasser,
    A continuation method for nonlinear regression,
    SIAM Journal of Numerical Analysis,
    Volume 18, pages 1139-1154, 1981.
  3. C. Fraley,
    Solution of nonlinear least-squares problems,
    Technical Report STAN-CS-1165,
    Computer Science Department,
    Stanford University, 1987.
  4. C. Fraley,
    Software performance on nonlinear least-squares problems,
    Technical Report SOL 88-17,
    Systems Optimization Laboratory,
    Department of Operations Research,
    Stanford University, 1988.
  5. JJ McKeown,
    Specialized versus general-purpose algorithms for functions that are sums of squared terms,
    Math. Prog.,
    Volume 9, pages 57-68, 1975.
  6. JJ McKeown,
    On algorithms for sums of squares problems,
    in Towards Global Optimization,
    L. C. W. Dixon and G. Szego (editors),
    North-Holland, pages 229-257, 1975.
  7. Jorge More, Burton Garbow, Kenneth Hillstrom,
    Testing unconstrained optimization software,
    ACM Transactions on Mathematical Software,
    Volume 7, Number 1, March 1981, pages 17-41.
  8. Jorge More, Burton Garbow, Kenneth Hillstrom,
    Algorithm 566: FORTRAN Subroutines for Testing unconstrained optimization software,
    ACM Transactions on Mathematical Software,
    Volume 7, Number 1, March 1981, pages 136-140.
  9. Douglas Salane,
    A continuation approach for solving large residual nonlinear least squares problems,
    SIAM Journal of Scientific and Statistical Computing,
    Volume 8, pages 655-671, 1987.

Source Code:

Last revised on 04 September 2020.