tblite_fit_newuoa Module Reference

NEWUOA: NEW **U**nconstrained **O**ptimization **A**lgorithm. More...

Data Types
interface	objective_function

Functions/Subroutines
subroutine, public	newuoa (n, npt, x, rhobeg, rhoend, iprint, maxfun, calfun, handle, error)
	This subroutine seeks the least value of a function of many variables, by a trust region method that forms quadratic models by interpolation. There can be some freedom in the interpolation conditions, which is taken up by minimizing the Frobenius norm of the change to the second.

Detailed Description

NEWUOA: NEW **U**nconstrained **O**ptimization **A**lgorithm.

The purpose of NEWUOA is to seek the least value of a function F of several variables, when derivatives are not available. The main new feature of the method is that quadratic models are updated using only about NPT=2N+1 interpolation conditions, the remaining freedom being taken up by minimizing the Frobenius norm of the change to the second derivative matrix of the model.

The new software was developed from [[UOBYQA]], which also forms quadratic models from interpolation conditions. That method requires NPT=(N+1)(N+2)/2 conditions, however, because they have to define all the parameters of the model. The least Frobenius norm updating procedure with NPT=2N+1 is usually much more efficient when N is large, because the work of each iteration is much less than before, and in some experiments the number of calculations of the objective function seems to be only of magnitude N.

References

• "[The NEWUOA software for unconstrained optimization without derivatives](http://www.damtp.cam.ac.uk/user/na/NA_papers/NA2004_08.pdf)", 2004/NA08
• "[The NEWUOA software for unconstrained minimization without derivatives](http://link.springer.com/chapter/10.1007%2F0-387-30065-1_16)", in Large-Scale Nonlinear Optimization, editors G. Di Pillo and M. Roma, Springer (2006), pages 255-297.

History

• M.J.D. Powell, December 16th, 2004 : It is hoped that the software will be helpful to much future research and to many applications. There are no restrictions on or charges for its use.
• Jacob Williams, July 2015 : refactoring of the code into modern Fortran.
• Sebastian Ehlert, August 2021 : removed implicit typing

@Inbook{Powell2006,
  author="Powell, M. J. D.",
  editor="Di Pillo, G.  and Roma, M.",
  title="The NEWUOA software for unconstrained optimization without derivatives",
  bookTitle="Large-Scale Nonlinear Optimization",
  year="2006",
  publisher="Springer US",
  address="Boston, MA",
  pages="255--297",
  url="https://doi.org/10.1007/0-387-30065-1_16"
}

Function/Subroutine Documentation

newuoa()

subroutine, public tblite_fit_newuoa::newuoa	(	integer, intent(in)	n,
		integer, intent(in)	npt,
		real(wp), dimension(*), intent(inout)	x,
		real(wp), intent(in)	rhobeg,
		real(wp), intent(in)	rhoend,
		integer, intent(in)	iprint,
		integer, intent(in)	maxfun,
		procedure(objective_function)	calfun,
		class(*), intent(in)	handle,
		type(error_type), intent(out), allocatable	error )

This subroutine seeks the least value of a function of many variables, by a trust region method that forms quadratic models by interpolation. There can be some freedom in the interpolation conditions, which is taken up by minimizing the Frobenius norm of the change to the second.

Parameters

[in]	n	The number of variables. Must be at least 2.
[in]	npt	The number of interpolation conditions. Its value must be in the interval [N+2, (N+1)(N+2)/2].
[in,out]	x	Initial values of the variables must be set in X(1), X(2), ..., X(N). They will be changed to the values that give the least calculated F.
[in]	rhobeg	RHOBEG and RHOEND must be set to the initial and final values of a trust region radius, so both must be positive with RHOEND<=RHOBEG. Typically RHOBEG should be about one tenth of the greatest expected change to a variable, and RHOEND should indicate the accuracy that is required in the final values of the variables.
[in]	rhoend	RHOBEG and RHOEND must be set to the initial and final values of a trust region radius, so both must be positive with RHOEND<=RHOBEG. Typically RHOBEG should be about one tenth of the greatest expected change to a variable, and RHOEND should indicate the accuracy that is required in the final values of the variables.
[in]	iprint	The value of IPRINT should be set to 0, 1, 2 or 3, which controls the amount of printing. Specifically, there is no output if IPRINT=0 and there is output only at the return if IPRINT=1. Otherwise, each new value of RHO is printed, with the best vector of variables so far and the corresponding value of the objective function. Further, each new value of F with its variables are output if IPRINT=3.
[in]	maxfun	An upper bound on the number of calls of CALFUN. It must set F to the value of the objective function for the variables X(1), X(2), ..., X(N).