Try out NAG Library functions

Explore NAG maths and stats routines with interactive demos
Function ID
Linear programming (LP) or convex quadratic programming (QP), sparse, active-set method, recommended
service routine | LP, linear programming | QP, quadratic programming | active-set method | sparse convex QP prolem
This example minimizes the quadratic function fx=cTx+12xTHx, where
subject to the bounds
and to the linear constraints
The example data reflects that shown in the "Example" section of the routine documentation. You can change this here to try alternative inputs. The formatting will need to be kept as it is here, otherwise the program is likely to fail to run correctly.

Please note that incompatible data will however cause the example output to display an error message. These error messages are fully explained in the Routine document
!   E04NQF Example Program Text
!   Mark 26.1 Release. NAG Copyright 2016.

    Module e04nqfe_mod

!     E04NQF Example Program Module:
!            Parameters and User-defined Routines

!     .. Use Statements ..
      Use nag_library, Only: nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Accessibility Statements ..
      Public                           :: qphx
!     .. Parameters ..
      Integer, Parameter, Public       :: lencw = 600, leniw = 600,            &
                                          lenrw = 600, nin = 5, nout = 6
      Subroutine qphx(ncolh,x,hx,nstate,cuser,iuser,ruser)
!       Routine to compute H*x. (In this version of QPHX, the Hessian
!       matrix H is not referenced explicitly.)

!       .. Scalar Arguments ..
        Integer, Intent (In)           :: ncolh, nstate
!       .. Array Arguments ..
        Real (Kind=nag_wp), Intent (Out) :: hx(ncolh)
        Real (Kind=nag_wp), Intent (Inout) :: ruser(*)
        Real (Kind=nag_wp), Intent (In) :: x(ncolh)
        Integer, Intent (Inout)        :: iuser(*)
        Character (8), Intent (Inout)  :: cuser(*)
!       .. Executable Statements ..
        hx(1) = 2.0E0_nag_wp*x(1)
        hx(2) = 2.0E0_nag_wp*x(2)
        hx(3) = 2.0E0_nag_wp*(x(3)+x(4))
        hx(4) = hx(3)
        hx(5) = 2.0E0_nag_wp*x(5)
        hx(6) = 2.0E0_nag_wp*(x(6)+x(7))
        hx(7) = hx(6)


      End Subroutine qphx
    End Module e04nqfe_mod
    Program e04nqfe

!     E04NQF Example Main Program

!     .. Use Statements ..
      Use e04nqfe_mod, Only: lencw, leniw, lenrw, nin, nout, qphx
      Use nag_library, Only: e04npf, e04nqf, e04ntf, nag_wp
!     .. Implicit None Statement ..
      Implicit None
!     .. Local Scalars ..
      Real (Kind=nag_wp)               :: obj, objadd, sinf
      Integer                          :: i, icol, ifail, iobj, jcol, lenc, m, &
                                          n, ncolh, ne, ninf, nname, ns
      Logical                          :: verbose_output
      Character (8)                    :: prob
      Character (1)                    :: start
!     .. Local Arrays ..
      Real (Kind=nag_wp), Allocatable  :: acol(:), bl(:), bu(:), c(:), pi(:),  &
                                          rc(:), x(:)
      Real (Kind=nag_wp)               :: ruser(1), rw(lenrw)
      Integer, Allocatable             :: helast(:), hs(:), inda(:), loca(:)
      Integer                          :: iuser(1), iw(leniw)
      Character (8)                    :: cuser(1), cw(lencw)
      Character (8), Allocatable       :: names(:)
!     .. Intrinsic Procedures ..
      Intrinsic                        :: max
!     .. Executable Statements ..
      Write (nout,*) 'E04NQF Example Program Results'

!     Skip heading in data file.
      Read (nin,*)

      Read (nin,*) n, m
      Read (nin,*) ne, iobj, ncolh, start, nname
      Allocate (inda(ne),loca(n+1),helast(n+m),hs(n+m),acol(ne),bl(n+m),       &

      Read (nin,*) names(1:nname)

!     Read the matrix ACOL from data file. Set up LOCA.

      jcol = 1
      loca(jcol) = 1

      Do i = 1, ne

!       Element ( INDA( I ), ICOL ) is stored in ACOL( I ).

        Read (nin,*) acol(i), inda(i), icol

        If (icol<jcol) Then

!         Elements not ordered by increasing column index.

          Write (nout,99998) 'Element in column', icol,                        &
            ' found after element in column', jcol, '. Problem', ' abandoned.'
          Go To 100
        Else If (icol==jcol+1) Then

!         Index in ACOL of the start of the ICOL-th column equals I.

          loca(icol) = i
          jcol = icol
        Else If (icol>jcol+1) Then

!         Index in ACOL of the start of the ICOL-th column equals I,
!         but columns JCOL+1,JCOL+2,...,ICOL-1 are empty. Set the
!         corresponding elements of LOCA to I.

          loca((jcol+1):icol) = i
          jcol = icol
        End If

      End Do

      loca(n+1) = ne + 1

!     Columns N,N-1,...,ICOL+1 are empty. Set the corresponding
!     elements of LOCA accordingly.

      Do i = n, icol + 1, -1
        loca(i) = loca(i+1)
      End Do

      Read (nin,*) bl(1:(n+m))
      Read (nin,*) bu(1:(n+m))

      If (start=='C') Then
        Read (nin,*) hs(1:n)
      Else If (start=='W') Then
        Read (nin,*) hs(1:(n+m))
      End If

      Read (nin,*) x(1:n)

      Write (nout,99999) n, m

!     Call E04NPF to initialize E04NQF.

      ifail = 0
      Call e04npf(cw,lencw,iw,leniw,rw,lenrw,ifail)

!     Set this to .True. to cause e04nqf to produce intermediate
!     progress output
      verbose_output = .False.

      If (verbose_output) Then
!       By default e04nqf does not print monitoring
!       information. Set the print file unit or the summary
!       file unit to get information.
        ifail = 0
        Call e04ntf('Print file',nout,cw,iw,rw,ifail)
      End If

!     We have no explicit objective vector so set LENC = 0; the
!     objective vector is stored in row IOBJ of ACOL.

      lenc = 0
      Allocate (c(max(1,lenc)))

      objadd = 0.0E0_nag_wp
      prob = ' '

!     Do not allow any elastic variables (i.e. they cannot be
!     infeasible). If we'd set optional argument "Elastic mode" to 0,
!     we wouldn't need to set the individual elements of array HELAST.

      helast(1:(n+m)) = 0

!     Solve the QP problem.

      ifail = 0
      Call e04nqf(start,qphx,m,n,ne,nname,lenc,ncolh,iobj,objadd,prob,acol,    &
        inda,loca,bl,bu,c,names,helast,hs,x,pi,rc,ns,ninf,sinf,obj,cw,lencw,   &

      Write (nout,*)
      Write (nout,99997) obj
      Write (nout,99996) x(1:n)

100   Continue

99999 Format (1X,/,1X,'QP problem contains ',I3,' variables and ',I3,          &
        ' linear constraints')
99998 Format (1X,A,I5,A,I5,A,A)
99997 Format (1X,'Final objective value = ',1P,E11.3)
99996 Format (1X,'Optimal X = ',7F9.2)

    End Program e04nqfe
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