NAG Library Manual, Mark 27.3
```!   E04WEF Example Program Text
!   Mark 27.3 Release. NAG Copyright 2021.

Module e04wefe_mod

!     E04WEF Example Program Module:
!            Parameters and User-defined Routines

!     .. Use Statements ..
Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Accessibility Statements ..
Private
Public                           :: confun, objfun
!     .. Parameters ..
Integer, Parameter, Public       :: leniw = 600, lenrw = 600, nin = 5,   &
ninopt = 7, nout = 6
Contains
!       Routine to evaluate objective function and its 1st derivatives.

!       .. Scalar Arguments ..
Real (Kind=nag_wp), Intent (Out) :: objf
Integer, Intent (Inout)        :: mode
Integer, Intent (In)           :: n, nstate
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (Inout) :: grad(n), ruser(*)
Real (Kind=nag_wp), Intent (In) :: x(n)
Integer, Intent (Inout)        :: iuser(*)
!       .. Executable Statements ..
If (mode==0 .Or. mode==2) Then
objf = x(1)*x(4)*(x(1)+x(2)+x(3)) + x(3)
End If

If (mode==1 .Or. mode==2) Then
End If

Return

End Subroutine objfun
Subroutine confun(mode,ncnln,n,ldcj,needc,x,ccon,cjac,nstate,iuser,      &
ruser)
!       Routine to evaluate the nonlinear constraints and their 1st
!       derivatives.

!       .. Scalar Arguments ..
Integer, Intent (In)           :: ldcj, n, ncnln, nstate
Integer, Intent (Inout)        :: mode
!       .. Array Arguments ..
Real (Kind=nag_wp), Intent (Out) :: ccon(max(1,ncnln))
Real (Kind=nag_wp), Intent (Inout) :: cjac(ldcj,n), ruser(*)
Real (Kind=nag_wp), Intent (In) :: x(n)
Integer, Intent (Inout)        :: iuser(*)
Integer, Intent (In)           :: needc(ncnln)
!       .. Intrinsic Procedures ..
Intrinsic                      :: max
!       .. Executable Statements ..
If (nstate==1) Then

!         First call to CONFUN.  Set all Jacobian elements to zero.
!         Note that this will only work when 'Derivative Level = 3'
!         (the default; see Section 11.2).

cjac(1:ncnln,1:n) = 0.0E0_nag_wp
End If

If (needc(1)>0) Then

If (mode==0 .Or. mode==2) Then
ccon(1) = x(1)**2 + x(2)**2 + x(3)**2 + x(4)**2
End If

If (mode==1 .Or. mode==2) Then
cjac(1,1) = 2.0E0_nag_wp*x(1)
cjac(1,2) = 2.0E0_nag_wp*x(2)
cjac(1,3) = 2.0E0_nag_wp*x(3)
cjac(1,4) = 2.0E0_nag_wp*x(4)
End If

End If

If (needc(2)>0) Then

If (mode==0 .Or. mode==2) Then
ccon(2) = x(1)*x(2)*x(3)*x(4)
End If

If (mode==1 .Or. mode==2) Then
cjac(2,1) = x(2)*x(3)*x(4)
cjac(2,2) = x(1)*x(3)*x(4)
cjac(2,3) = x(1)*x(2)*x(4)
cjac(2,4) = x(1)*x(2)*x(3)
End If

End If

Return

End Subroutine confun
End Module e04wefe_mod
Program e04wefe

!     E04WEF Example Main Program

!     .. Use Statements ..
Use e04wefe_mod, Only: confun, leniw, lenrw, nin, ninopt, nout, objfun
Use nag_library, Only: e04wcf, e04wdf, e04wef, e04wff, e04wgf, e04whf,   &
e04wkf, e04wlf, nag_wp, x04acf, x04baf
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Character (*), Parameter         :: fname = 'e04wefe.opt'
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: bndinf, featol, objf
Integer                          :: elmode, i, ifail, lda, ldcj, ldh,    &
majits, mode, n, nclin, ncnln, sda,  &
sdcjac
Character (80)                   :: rec
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), bl(:), bu(:), ccon(:),       &
h(:,:), x(:)
Real (Kind=nag_wp)               :: ruser(1), rw(lenrw)
Integer, Allocatable             :: istate(:)
Integer                          :: iuser(1), iw(leniw)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max
!     .. Executable Statements ..
Write (rec,99995) 'E04WEF Example Program Results'
Call x04baf(nout,rec)

!     This program demonstrates the use of routines to set and
!     get values of optional parameters associated with E04WDF.

!     Skip heading in data file

lda = max(1,nclin)

If (nclin>0) Then
sda = n
Else
sda = 1
End If

ldcj = max(1,ncnln)

If (ncnln>0) Then
sdcjac = n
Else
sdcjac = 1
End If

ldh = n
Allocate (istate(n+nclin+ncnln),a(lda,sda),bl(n+nclin+ncnln),            &
bu(n+nclin+ncnln),ccon(max(1,ncnln)),cjac(ldcj,sdcjac),clamda(n+nclin+ &

If (nclin>0) Then
End If

!     Call E04WCF to initialize E04WDF.

ifail = 0
Call e04wcf(iw,leniw,rw,lenrw,ifail)

!     By default E04WDF does not print monitoring
!     information. Set the print file unit or the summary
!     file unit to get information.

ifail = 0
Call e04wgf('Print file',nout,iw,rw,ifail)

!     Open the options file for reading

mode = 0

ifail = 0
Call x04acf(ninopt,fname,mode,ifail)

!     Use E04WEF to read some options from the options file

ifail = 0
Call e04wef(ninopt,iw,rw,ifail)

Write (rec,'()')
Call x04baf(nout,rec)

!     Use E04WKF to find the value of integer-valued option
!     'Elastic mode'.

ifail = 0
Call e04wkf('Elastic mode',elmode,iw,rw,ifail)

Write (rec,99999) elmode
Call x04baf(nout,rec)

!     Use E04WHF to set the value of real-valued option
!     'Infinite bound size'.

bndinf = 1.0E10_nag_wp

ifail = 0
Call e04whf('Infinite bound size',bndinf,iw,rw,ifail)

!     Use E04WLF to find the value of real-valued option
!     'Feasibility tolerance'.

ifail = 0
Call e04wlf('Feasibility tolerance',featol,iw,rw,ifail)

Write (rec,99998) featol
Call x04baf(nout,rec)

!     Use E04WFF to set the option 'Major iterations limit'.

ifail = 0
Call e04wff('Major iterations limit 50',iw,rw,ifail)

!     Solve the problem.

ifail = 0
Call e04wdf(n,nclin,ncnln,lda,ldcj,ldh,a,bl,bu,confun,objfun,majits,     &
ifail)

Write (rec,'()')
Call x04baf(nout,rec)
Write (rec,99997) objf
Call x04baf(nout,rec)
Write (rec,99996)(x(i),i=1,n)
Call x04baf(nout,rec)

99999 Format (1X,'Option ''Elastic mode'' has the value ',I3,'.')
99998 Format (1X,'Option ''Feasibility tolerance'' has the value ',1P,E13.5,   &
'.')
99997 Format (1X,'Final objective value = ',F11.3)
99996 Format (1X,'Optimal X = ',7F9.2)
99995 Format (1X,A)
End Program e04wefe
```