# Try out NAG Library functions

Explore NAG maths and stats routines with interactive demos
Function ID
E04MFF
Name
nagf_opt_lp_solve_old
Description
Linear programming
Keywords
LP, linear programming | active-set method
This example minimizes the function
 $-0.02x1-0.2x2-0.2x3-0.2x4-0.2x5+0.04x6+0.04x7$
subject to the bounds
 $-0.01≤x1≤0.01-0.10≤x2≤0.15-0.01≤x3≤0.03-0.04≤x4≤0.02-0.10≤x5≤0.05-0.01≤x6≤0.00-0.01≤x7≤0.00$
and the general constraints
 $x1+x2+x3+x4+x5+x6+x7=-0.130.15x1+0.04x2+0.02x3+0.04x4+0.02x5+0.01x6+0.03x7≤-0.00490.03x1+0.05x2+0.08x3+0.02x4+0.06x5+0.01x6≤-0.006400.02x1+0.04x2+0.01x3+0.02x4+0.02x5≤-0.00370.02x1+0.03x2+0.01x5≤-0.0012-0.0992≤0.70x1+0.75x2+0.80x3+0.75x4+0.80x5+0.97x6-0.003≤0.02x1+0.06x2+0.08x3+0.12x4+0.02x5+0.01x6+0.97x7≤-0.002$
    Program e04mffe

!     E04MFF Example Program Text

!     Mark 26.1 Release. NAG Copyright 2016.

!     .. Use Statements ..
Use nag_library, Only: e04mff, e04mhf, nag_wp
!     .. Implicit None Statement ..
Implicit None
!     .. Parameters ..
Integer, Parameter               :: nin = 5, nout = 6
!     .. Local Scalars ..
Real (Kind=nag_wp)               :: obj
Integer                          :: i, ifail, iter, j, lda, liwork,      &
lwork, n, nclin, sda
Logical                          :: verbose_output
!     .. Local Arrays ..
Real (Kind=nag_wp), Allocatable  :: a(:,:), ax(:), bl(:), bu(:),         &
clamda(:), cvec(:), work(:), x(:)
Integer, Allocatable             :: istate(:), iwork(:)
!     .. Intrinsic Procedures ..
Intrinsic                        :: max
!     .. Executable Statements ..
Write (nout,*) 'E04MFF Example Program Results'

!     Skip heading in data file

Read (nin,*) n, nclin
liwork = 2*n + 3

!     The minimum LWORK for an LP problem:

If (0<nclin .And. nclin<n) Then
lwork = 2*(nclin+1)**2 + 7*n + 5*nclin
Else If (nclin>=n) Then
lwork = 2*n**2 + 7*n + 5*nclin
Else
lwork = 7*n + 1
End If

lda = max(1,nclin)

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

Allocate (istate(n+nclin),iwork(liwork),a(lda,sda),bl(n+nclin),          &
bu(n+nclin),cvec(n),x(n),ax(max(1,nclin)),clamda(n+nclin),work(lwork))

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

If (.Not. verbose_output) Then
!       Turn off intermediate output from e04mff - it is on by default
Call e04mhf('Nolist')
Call e04mhf('Print Level = 0')
End If

!     Solve the problem

ifail = 0
Call e04mff(n,nclin,a,lda,bl,bu,cvec,istate,x,iter,obj,ax,clamda,iwork,  &
liwork,work,lwork,ifail)

Select Case (ifail)
Case (0:5,7:)
Write (nout,*)
Write (nout,99999)
Do i = 1, n
Write (nout,99998) i, istate(i), x(i), clamda(i)
End Do

If (nclin>0) Then
Write (nout,*)
Write (nout,99997)
Do i = n + 1, n + nclin
j = i - n
Write (nout,99996) j, istate(i), ax(j), clamda(i)
End Do

End If

Write (nout,*)
Write (nout,99995) obj
End Select

99999 Format (1X,'Varbl',3X,'Istate',4X,'Value',9X,'Lagr Mult')
99998 Format (1X,'V',2(1X,I3),4X,1P,E14.3,2X,1P,E12.3)
99997 Format (1X,'L Con',3X,'Istate',4X,'Value',9X,'Lagr Mult')
99996 Format (1X,'L',2(1X,I3),4X,1P,E14.3,2X,1P,E12.3)
99995 Format (1X,'Final objective value = ',1P,E15.3)
End Program e04mffe

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