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:

Linear function, full rank

Linear function, rank 1.

Linear function, rank 1, zero columns and rows.

Rosenbrock function.

Helical valley function.

Powell singular function.

Freudenstein/Roth function.

Bard function.

Kowalik and Osborne function.

Meyer function.

Watson function.

Box 3dimensional function.

Jennrich and Sampson function.

Brown and Dennis function.

Chebyquad function.

Brown almostlinear function.

Osborne function 1.

Osborne function 2.

Hanson function 1

Hanson function 2

McKeown function 1

McKeown function 2

McKeown function 3

Devilliers and Glasser function 1

Devilliers and Glasser function 2

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:

John Dennis, David Gay, and Phuong Vu,
A new nonlinear equations test problem,
Technical Report 8316,
Mathematical Sciences Department,
Rice University, (1983  revised 1985).

N. de Villiers and D. Glasser,
A continuation method for nonlinear regression,
SIAM Journal of Numerical Analysis,
Volume 18, pages 11391154, 1981.

C. Fraley,
Solution of nonlinear leastsquares problems,
Technical Report STANCS1165,
Computer Science Department,
Stanford University, 1987.

C. Fraley,
Software performance on nonlinear leastsquares problems,
Technical Report SOL 8817,
Systems Optimization Laboratory,
Department of Operations Research,
Stanford University, 1988.

JJ McKeown,
Specialized versus generalpurpose algorithms for functions that
are sums of squared terms,
Math. Prog.,
Volume 9, pages 5768, 1975.

JJ McKeown,
On algorithms for sums of squares problems,
in Towards Global Optimization,
L. C. W. Dixon and G. Szego (editors),
NorthHolland, pages 229257, 1975.

Jorge More, Burton Garbow, Kenneth Hillstrom,
Testing unconstrained optimization software,
ACM Transactions on Mathematical Software,
Volume 7, Number 1, March 1981, pages 1741.

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 136140.

Douglas Salane,
A continuation approach for solving large residual nonlinear
least squares problems,
SIAM Journal of Scientific and Statistical Computing,
Volume 8, pages 655671, 1987.
Source Code:
Last revised on 04 September 2020.