! E04SRF Example Program Text
! Mark 30.2 Release. NAG Copyright 2024.
! NLP example: Nonlinear objective, linear constraint and two nonlinear
! constraints.
Module e04srfe_mod
! .. Use Statements ..
Use nag_precisions, Only: wp
! .. Implicit None Statement ..
Implicit None
! .. Accessibility Statements ..
Private
Public :: confun, congrd, objfun, objgrd
Contains
Subroutine objfun(nvar,x,fx,inform,iuser,ruser,cpuser)
! .. Use Statements ..
Use, Intrinsic :: iso_c_binding, Only: c_ptr
! .. Implicit None Statement ..
Implicit None
! .. Scalar Arguments ..
Type (c_ptr), Intent (In) :: cpuser
Real (Kind=wp), Intent (Out) :: fx
Integer, Intent (Inout) :: inform
Integer, Intent (In) :: nvar
! .. Array Arguments ..
Real (Kind=wp), Intent (Inout) :: ruser(*)
Real (Kind=wp), Intent (In) :: x(nvar)
Integer, Intent (Inout) :: iuser(*)
! .. Intrinsic Procedures ..
Intrinsic :: cos
! .. Executable Statements ..
Continue
fx = (x(1)+x(2)+x(3))**2 + 3.0_wp*x(3) + 5.0_wp*x(4) + &
cos(0.01_wp*x(1)) - 1.0_wp
inform = 0
End Subroutine objfun
Subroutine objgrd(nvar,x,nnzfd,fdx,inform,iuser,ruser,cpuser)
! .. Use Statements ..
Use, Intrinsic :: iso_c_binding, Only: c_ptr
! .. Implicit None Statement ..
Implicit None
! .. Scalar Arguments ..
Type (c_ptr), Intent (In) :: cpuser
Integer, Intent (Inout) :: inform
Integer, Intent (In) :: nnzfd, nvar
! .. Array Arguments ..
Real (Kind=wp), Intent (Inout) :: fdx(nnzfd), ruser(*)
Real (Kind=wp), Intent (In) :: x(nvar)
Integer, Intent (Inout) :: iuser(*)
! .. Local Scalars ..
Real (Kind=wp) :: s
! .. Intrinsic Procedures ..
Intrinsic :: sin
! .. Executable Statements ..
Continue
s = 2.0_wp*(x(1)+x(2)+x(3))
fdx(1) = s - 0.01*sin(x(1))
fdx(2) = s
fdx(3) = s + 3.0_wp
fdx(4) = 5.0_wp
inform = 0
End Subroutine objgrd
Subroutine confun(nvar,x,ng,gx,inform,iuser,ruser,cpuser)
! .. Use Statements ..
Use, Intrinsic :: iso_c_binding, Only: c_ptr
! .. Implicit None Statement ..
Implicit None
! .. Scalar Arguments ..
Type (c_ptr), Intent (In) :: cpuser
Integer, Intent (Inout) :: inform
Integer, Intent (In) :: ng, nvar
! .. Array Arguments ..
Real (Kind=wp), Intent (Out) :: gx(ng)
Real (Kind=wp), Intent (Inout) :: ruser(*)
Real (Kind=wp), Intent (In) :: x(nvar)
Integer, Intent (Inout) :: iuser(*)
! .. Executable Statements ..
Continue
gx(1) = x(1)**2 + x(2)**2 + x(3)
gx(2) = x(2)**4 + x(4)
inform = 0
End Subroutine confun
Subroutine congrd(nvar,x,nnzfd,gdx,inform,iuser,ruser,cpuser)
! .. Use Statements ..
Use, Intrinsic :: iso_c_binding, Only: c_ptr
! .. Implicit None Statement ..
Implicit None
! .. Scalar Arguments ..
Type (c_ptr), Intent (In) :: cpuser
Integer, Intent (Inout) :: inform
Integer, Intent (In) :: nnzfd, nvar
! .. Array Arguments ..
Real (Kind=wp), Intent (Inout) :: gdx(nnzfd), ruser(*)
Real (Kind=wp), Intent (In) :: x(nvar)
Integer, Intent (Inout) :: iuser(*)
! .. Executable Statements ..
Continue
gdx(1) = 2.0_wp*x(1)
gdx(2) = 2.0_wp*x(2)
gdx(3) = 1.0_wp
gdx(4) = 4.0_wp*x(2)**3
gdx(5) = 1.0_wp
inform = 0
End Subroutine congrd
End Module e04srfe_mod
Program e04srfe
! .. Use Statements ..
Use e04srfe_mod, Only: confun, congrd, objfun, objgrd
Use, Intrinsic :: iso_c_binding, Only: c_null_ptr, &
c_ptr
Use nag_library, Only: e04raf, e04rcf, e04rgf, e04rhf, e04rjf, e04rkf, &
e04rzf, e04srf, e04sru, e04srz, e04zmf
Use nag_precisions, Only: wp
! .. Implicit None Statement ..
Implicit None
! .. Parameters ..
Real (Kind=wp), Parameter :: bigbnd = 1.0E20_wp
Integer, Parameter :: nout = 6
! .. Local Scalars ..
Type (c_ptr) :: cpuser, handle
Integer :: i, idlc, ifail, inform, nclin, &
ncnln, nnzb, nnzfd, nnzgd, nnzu, &
nvar
Character (6) :: rlmtest
! .. Local Arrays ..
Real (Kind=wp), Allocatable :: b(:), blx(:), bux(:), fdx(:), fl(:), &
fu(:), gdx(:), lambda(:), lcbl(:), &
lcbu(:), lmtest(:), u(:), x(:)
Real (Kind=wp) :: rinfo(100), ruser(0), stats(100)
Integer, Allocatable :: icolb(:), icolgd(:), iidx(:), &
irowb(:), irowgd(:)
Integer :: iuser(0)
! .. Intrinsic Procedures ..
Intrinsic :: abs, int, merge
! .. Executable Statements ..
ifail = 0
cpuser = c_null_ptr
Write (nout,Fmt=99999) 'E04SRF Example Program Results'
! Problem size
nvar = 4
! Counter for Lagrange multipliers
nnzu = 0
Allocate (x(nvar),blx(nvar),bux(nvar))
! Initialize handle
ifail = 0
Call e04raf(handle,nvar,ifail)
! Add simple box bounds on x
blx(1:nvar) = (/-bigbnd,-bigbnd,0.0_wp,0.0_wp/)
bux(1:nvar) = bigbnd
ifail = 0
Call e04rhf(handle,nvar,blx,bux,ifail)
! Specify the amount of Lagrange mult. required
nnzu = 2*nvar
! Add nonlinear objective gradient information
nnzfd = nvar
Allocate (iidx(nnzfd),fdx(nnzfd))
iidx(:) = (/(i,i=1,nvar)/)
ifail = 0
Call e04rgf(handle,nnzfd,iidx,ifail)
! Add two nonlinear constraints
ncnln = 2
Allocate (fl(ncnln),fu(ncnln))
fl(:) = (/2.0_wp,4.0_wp/)
fu(:) = (/2.0_wp,4.0_wp/)
! Number of nonzero elements in the constraint Jacobian
nnzgd = 5
Allocate (irowgd(nnzgd),icolgd(nnzgd),gdx(nnzgd))
irowgd(:) = (/1,1,1,2,2/)
icolgd(:) = (/1,2,3,2,4/)
! Add nonlinear constraint information
ifail = 0
Call e04rkf(handle,ncnln,fl,fu,nnzgd,irowgd,icolgd,ifail)
! Update the Lagrange mult. count
nnzu = nnzu + 2*ncnln
! Add one linear constraint
nclin = 1
! Number of nonzero elements in the constraint
nnzb = 2
Allocate (lcbl(nclin),lcbu(nclin),irowb(nnzb),icolb(nnzb),b(nnzb))
lcbl(1) = 0.0_wp
lcbu(1) = bigbnd
irowb(:) = (/1,1/)
icolb(:) = (/1,2/)
b(:) = (/2.0_wp,4.0_wp/)
idlc = 0
ifail = 0
Call e04rjf(handle,nclin,lcbl,lcbu,nnzb,irowb,icolb,b,idlc,ifail)
! Update the Lagrange mult. count
nnzu = nnzu + 2*nclin
Allocate (u(nnzu))
! Optionally, define variable x(4) to be linear
! Hinting which variables are linear in problems with many
! variables can speed up performance
Call e04rcf(handle,'linear',1,(/4/),ifail)
! Define initial guess point
x(1:nvar) = (/1.0_wp,2.0_wp,3.0_wp,4.0_wp/)
! Add options
ifail = 0
! Disable printing
Call e04zmf(handle,'Print Level = 0',ifail)
! Do not print options
Call e04zmf(handle,'Print Options = No',ifail)
! It is recommended on new problems to always verify the derivatives
Call e04zmf(handle,'Verify Derivatives = Yes',ifail)
! Do not print solution, x and f(x) will be printed afterwards
Call e04zmf(handle,'Print Solution = No',ifail)
! Solve the problem
ifail = -1
Call e04srf(handle,objfun,objgrd,confun,congrd,e04srz,e04sru,nvar,x, &
nnzu,u,rinfo,stats,iuser,ruser,cpuser,ifail)
Allocate (lambda(nnzu/2),lmtest(nnzfd))
If (ifail==0) Then
! Print solution point and objective function value
Write (nout,99998)
Write (nout,99993)(i,x(i),i=1,nvar)
Write (nout,99997)
Write (nout,99990)(i,u(2*i-1),i,u(2*i),i=1,nvar)
Write (nout,99995)
Write (nout,99991)(i,u(2*i-1+2*nvar),i,u(2*i+2*nvar),i=1,nclin)
Write (nout,99994)
Write (nout,99991)(i,u(2*i-1+2*nvar+2*nclin),i,u(2*i+2*nvar+2*nclin), &
i=1,ncnln)
! Gradient of the objective
inform = 0
Call objgrd(nvar,x,nnzfd,fdx,inform,iuser,ruser,cpuser)
! Gradient of the linear constraints is already available in
! irowb(1:2), icolb(1:2) and b(1:2)
! Gradient of the nonlinear constraint
Call congrd(nvar,x,nnzgd,gdx,ifail,iuser,ruser,cpuser)
! Check of Lagrange multipliers (complementarity)
! Obtain the multipliers with correct sign
! 4 bound constraints, 1 linear constraints, and 2 nonlinear constraints
Do i = 1, 7
lambda(i) = u(2*i) - u(2*i-1)
End Do
! lambda (1..4) mult. related to bounds
! lambda (5) mult. related to linear constraints
! lambda (6..7) mult. related to the nonlinear constraint
Write (nout,99996)
lmtest(1) = fdx(1) + lambda(1) + lambda(5)*b(1) + lambda(6)*gdx(1)
lmtest(2) = fdx(2) + lambda(2) + lambda(5)*b(2) + lambda(6)*gdx(2) + &
lambda(7)*gdx(4)
lmtest(3) = fdx(3) + lambda(3) + lambda(6)*gdx(3)
lmtest(4) = fdx(4) + lambda(4) + lambda(7)*gdx(5)
Do i = 1, 4
rlmtest = merge('Ok ','Failed',abs(lmtest(i))<2.5E-8_wp)
Write (nout,99992) i, lmtest(i), rlmtest
End Do
Write (nout,99989) rinfo(1)
Write (nout,99988) rinfo(2)
Write (nout,99987) rinfo(3)
Write (nout,99986) int(stats(1))
Write (nout,99985) int(stats(19))
Write (nout,99984) int(stats(5))
Write (nout,99983) int(stats(20))
Write (nout,99982) int(stats(21))
Write (nout,99981) int(stats(4))
End If
Flush (nout)
! Clean up
ifail = 0
Call e04rzf(handle,ifail)
Deallocate (b,blx,bux,fl,fu,lcbl,lcbu,u,x,lambda,fdx,gdx,lmtest,icolb, &
icolgd,iidx,irowb,irowgd)
99999 Format (A)
99998 Format (/,'Variables')
99997 Format ('Variable bound Lagrange multipliers')
99996 Format ('Stationarity test for Lagrange multipliers')
99995 Format ('Linear constraint Lagrange multipliers')
99994 Format ('Nonlinear constraints Lagrange multipliers')
99993 Format (5X,'x(',I10,')',17X,'=',1P,E16.2)
99992 Format (4X,'lx(',I10,')',17X,'=',1P,E16.2,5X,A6)
99991 Format (4X,'zL(',I10,')',17X,'=',1P,E16.2,/,4X,'zU(',I10,')',17X,'=',1P, &
E16.2)
99990 Format (4X,'zL(',I10,')',17X,'=',1P,E16.2,/,4X,'zU(',I10,')',17X,'=',1P, &
E16.2)
99989 Format (/,'Solution found. Objective minimum =',1P,E16.4)
99988 Format (' Constraint violation =',1P,6X,E10.2)
99987 Format (' Dual infeasibility =',1P,6X,E10.2)
99986 Format (' Iterations =',5X,I11)
99985 Format (' Objective evaluations =',5X,I11)
99984 Format (' Objective gradient evaluations =',5X,I11)
99983 Format (' Constraint evaluations =',5X,I11)
99982 Format (' Constraint gradient evaluations =',5X,I11)
99981 Format (' Hessian evaluations =',5X,I11)
End Program e04srfe