File: driver3.f90

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!                                                                                      
!  L-BFGS-B is released under the “New BSD License” (aka “Modified BSD License”        
!  or “3-clause license”)                                                              
!  Please read attached file License.txt                                               
!                                        
!                             DRIVER 3  in Fortran 90
!     --------------------------------------------------------------
!            TIME-CONTROLLED DRIVER FOR L-BFGS-B 
!     --------------------------------------------------------------
!
!        L-BFGS-B is a code for solving large nonlinear optimization
!             problems with simple bounds on the variables.
!
!        The code can also be used for unconstrained problems and is
!        as efficient for these problems as the earlier limited memory
!                          code L-BFGS.
!
!        This driver shows how to terminate a run after some prescribed
!        CPU time has elapsed, and how to print the desired information 
!        before exiting.
!
!     References:
!
!        [1] R. H. Byrd, P. Lu, J. Nocedal and C. Zhu, ``A limited
!        memory algorithm for bound constrained optimization'',
!        SIAM J. Scientific Computing 16 (1995), no. 5, pp. 1190--1208.
!
!        [2] C. Zhu, R.H. Byrd, P. Lu, J. Nocedal, ``L-BFGS-B: FORTRAN
!        Subroutines for Large Scale Bound Constrained Optimization''
!        Tech. Report, NAM-11, EECS Department, Northwestern University,
!        1994.
!
!
!          (Postscript files of these papers are available via anonymous
!           ftp to eecs.nwu.edu in the directory pub/lbfgs/lbfgs_bcm.)
!
!                              *  *  *
!
!         February 2011   (latest revision)
!         Optimization Center at Northwestern University
!         Instituto Tecnologico Autonomo de Mexico
!
!         Jorge Nocedal and Jose Luis Morales
!
!     **************

      program driver

!     This time-controlled driver shows that it is possible to terminate
!     a run by elapsed CPU time, and yet be able to print all desired
!     information. This driver also illustrates the use of two
!     stopping criteria that may be used in conjunction with a limit
!     on execution time. The sample problem used here is the same as in 
!     driver1 and driver2 (the extended Rosenbrock function with bounds 
!     on the variables).

      implicit none

!     We specify a limit on the CPU time (tlimit = 10 seconds)
!
!     We suppress the default output (iprint = -1). The user could 
!       also elect to use the default output by choosing iprint >= 0.)
!     We suppress the code-supplied stopping tests because we will
!       provide our own termination conditions
!     We specify the dimension n of the sample problem and the number
!        m of limited memory corrections stored. 

      integer,  parameter    :: n = 1000, m = 10, iprint = -1
      integer,  parameter    :: dp = kind(1.0d0)
      real(dp), parameter    :: factr  = 0.0d0, pgtol  = 0.0d0, &
                                tlimit = 10.0d0
!
      character(len=60)      :: task, csave
      logical                :: lsave(4)
      integer                :: isave(44)
      real(dp)               :: f
      real(dp)               :: dsave(29)
      integer,  allocatable  :: nbd(:), iwa(:)
      real(dp), allocatable  :: x(:), l(:), u(:), g(:), wa(:)
!
      real(dp)               :: t1, t2, time1, time2
      integer                :: i, j

      allocate ( nbd(n), x(n), l(n), u(n), g(n) )
      allocate ( iwa(3*n) )
      allocate ( wa(2*m*n + 5*n + 11*m*m + 8*m) )

!     This time-controlled driver shows that it is possible to terminate
!     a run by elapsed CPU time, and yet be able to print all desired
!     information. This driver also illustrates the use of two
!     stopping criteria that may be used in conjunction with a limit
!     on execution time. The sample problem used here is the same as in 
!     driver1 and driver2 (the extended Rosenbrock function with bounds 
!     on the variables).
 
!     We now specify nbd which defines the bounds on the variables:
!                    l   specifies the lower bounds,
!                    u   specifies the upper bounds. 
 
!     First set bounds on the odd-numbered variables.

      do 10 i=1, n,2
         nbd(i)=2
         l(i)=1.0d0
         u(i)=1.0d2
  10  continue

!     Next set bounds on the even-numbered variables.

      do 12 i=2, n,2
         nbd(i)=2
         l(i)=-1.0d2
         u(i)=1.0d2
  12   continue

!     We now define the starting point.

      do 14 i=1, n
         x(i)=3.0d0
  14  continue
 
!     We now write the heading of the output.

      write (6,16)
  16  format(/,5x, 'Solving sample problem.',&
             /,5x, ' (f = 0.0 at the optimal solution.)',/) 

!     We start the iteration by initializing task.
 
      task = 'START'

!        ------- the beginning of the loop ----------

!     We begin counting the CPU time.

      call timer(time1)

      do while( task(1:2).eq.'FG'.or.task.eq.'NEW_X'.or. &
                task.eq.'START')
      
!     This is the call to the L-BFGS-B code.
 
         call setulb(n,m,x,l,u,nbd,f,g,factr,pgtol,wa,iwa, &
                     task,iprint, csave,lsave,isave,dsave)
 
         if (task(1:2) .eq. 'FG') then

!        the minimization routine has returned to request the
!        function f and gradient g values at the current x.
!        Before evaluating f and g we check the CPU time spent.

         call timer(time2)
         if (time2-time1 .gt. tlimit) then
            task='STOP: CPU EXCEEDING THE TIME LIMIT.'

!          Note: Assigning task(1:4)='STOP' will terminate the run;
!          setting task(7:9)='CPU' will restore the information at
!          the latest iterate generated by the code so that it can
!          be correctly printed by the driver.

!          In this driver we have chosen to disable the
!          printing options of the code (we set iprint=-1);
!          instead we are using customized output: we print the
!          latest value of x, the corresponding function value f and
!          the norm of the projected gradient |proj g|.

!          We print out the information contained in task.

              write (6,*) task

!          We print the latest iterate contained in wa(j+1:j+n), where
 
              j = 3*n+2*m*n+11*m**2
              write (6,*) 'Latest iterate X ='
              write (6,'((1x,1p, 6(1x,d11.4)))') (wa(i),i = j+1,j+n) 

!          We print the function value f and the norm of the projected
!          gradient |proj g| at the last iterate; they are stored in
!          dsave(2) and dsave(13) respectively.

              write (6,'(a,1p,d12.5,4x,a,1p,d12.5)') &
              'At latest iterate   f =',dsave(2),'|proj g| =',dsave(13)
            else

!          The time limit has not been reached and we compute
!          the function value f for the sample problem.

              f=.25d0*(x(1)-1.d0)**2
              do 20 i=2, n
                 f=f+(x(i)-x(i-1)**2)**2
  20          continue
              f=4.d0*f

!          Compute gradient g for the sample problem.

               t1 = x(2) - x(1)**2
               g(1) = 2.d0*(x(1)-1.d0)-1.6d1*x(1)*t1
               do 22 i=2,n-1
                  t2=t1
                  t1=x(i+1)-x(i)**2
                  g(i)=8.d0*t2-1.6d1*x(i)*t1
  22           continue
               g(n)=8.d0*t1
            endif

!          go back to the minimization routine.
         else

           if (task(1:5) .eq. 'NEW_X') then        

!        the minimization routine has returned with a new iterate.
!        The time limit has not been reached, and we test whether
!        the following two stopping tests are satisfied:

!        1) Terminate if the total number of f and g evaluations
!             exceeds 900.

            if (isave(34) .ge. 900) &
            task='STOP: TOTAL NO. of f AND g EVALUATIONS EXCEEDS LIMIT'

!        2) Terminate if  |proj g|/(1+|f|) < 1.0d-10.

            if (dsave(13) .le. 1.d-10*(1.0d0 + abs(f))) &
            task='STOP: THE PROJECTED GRADIENT IS SUFFICIENTLY SMALL'

!        We wish to print the following information at each iteration:
!          1) the current iteration number, isave(30),
!          2) the total number of f and g evaluations, isave(34),
!          3) the value of the objective function f,
!          4) the norm of the projected gradient,  dsve(13)
!
!        See the comments at the end of driver1 for a description
!        of the variables isave and dsave.
         
            write (6,'(2(a,i5,4x),a,1p,d12.5,4x,a,1p,d12.5)') 'Iterate' &
            ,isave(30),'nfg =',isave(34),'f =',f,'|proj g| =',dsave(13)

!        If the run is to be terminated, we print also the information
!        contained in task as well as the final value of x.

            if (task(1:4) .eq. 'STOP') then
               write (6,*) task  
               write (6,*) 'Final X='
               write (6,'((1x,1p, 6(1x,d11.4)))') (x(i),i = 1,n)
            endif

          endif
        end if 
      end do
 
!     If task is neither FG nor NEW_X we terminate execution.

      end program driver

!======================= The end of driver3 ============================