```!   E04FGF Example Program Text

Program e04fgfe

!     Mark 27.0 Release. NAG Copyright 2019.

!     .. Use Statements ..
Use iso_c_binding, Only: c_ptr
Use nag_library, Only: e04fgf, e04raf, e04rhf, e04rmf, e04rzf, e04zmf,   &
nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Real (Kind=nag_wp), Parameter    :: infbnd = 1.0E20_nag_wp
Integer, Parameter               :: nout = 6
!     .. Local Scalars ..
Type (c_ptr)                     :: handle
Integer                          :: i, ifail, irevcm, isparse, maxeval,  &
neval, nnzrd, nres, nvar
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: lx(:), rx(:,:), ux(:), x(:,:)
Real (Kind=nag_wp)               :: rinfo(100), stats(100)
Integer                          :: icolrd(1), irowrd(1)
!     .. Executable Statements ..

Write (nout,*) 'E04FGF Example Program Results'
Write (nout,*)
Flush (nout)

nvar = 2
nres = 2
maxeval = 2

!     Initialize handle
ifail = 0
Call e04raf(handle,nvar,ifail)

!     Define residuals structure, isparse=0 means the residual structure is
!     dense => irowrd and icolrd are not accessed
isparse = 0
nnzrd = 1
Call e04rmf(handle,nres,isparse,nnzrd,irowrd,icolrd,ifail)

!     Set options
!     relax the main convergence criteria a bit
Call e04zmf(handle,'DFO Trust Region Tolerance = 5.0e-6',ifail)
!     Print the solution
Call e04zmf(handle,'Print Solution = YES',ifail)

!     Define starting point
Allocate (x(nvar,maxeval),rx(nres,maxeval))
x(1:2,1) = (/-1.2_nag_wp,1.0_nag_wp/)

!     Define bounds for the second and the fourth variable
Allocate (lx(nvar),ux(nvar))
lx(1:2) = (/-1.5_nag_wp,-2.0_nag_wp/)
ux(1:2) = (/2.0_nag_wp,infbnd/)
Call e04rhf(handle,nvar,lx,ux,ifail)

!     Call the solver in the reverse communication loop
irevcm = 1
Do While (irevcm/=0)
ifail = -1
Call e04fgf(handle,irevcm,neval,maxeval,nvar,x,nres,rx,rinfo,stats,    &
ifail)
If (irevcm==1) Then
Do i = 1, neval
!           Compute the rosenbrock objective function on the required points
rx(1,i) = 1.0_nag_wp - x(1,i)
rx(2,i) = 10.0_nag_wp*(x(2,i)-x(1,i)**2)
End Do
End If
End Do

!     Free the handle memory
ifail = 0
Call e04rzf(handle,ifail)

End Program e04fgfe
```