!************************************************************************* !* * !* LDGBM - Limited Memory (Discrete Gradient) Bundle Method * !* for Nonsmooth Nonconvex Optimization * !* * !* * !* by Napsu Karmitsa 2011 (last modified 2011) * !* * !* * !* The software is free for academic teaching and research * !* purposes but I ask you to refer the reference * !* given below, if you use it. * !* * !************************************************************************* !* !* !* Codes included in LDGBM: !* !* tldgbm.f95 - mainprogram for LDGBM (this file). !* initialization.f95 - user-specified initial values for parameters !* and starting point x. !* ldgbm_objfun.f95 - user-specified computation of the objective. !* function value (and the subgradient). !* parameters.f95 - parameters. !* ldgbm.f95 - limited memory disgrete gradient bundle method. !* lmbm.f95 - limited memory bundle method. !* ldgbm_sub.f95 - subprograms for limited memory bundle method. !* Makefile - makefile. !* !* tnsunc.f95 - large-scale nonsmooth test problems. !* !* To use the software modify tldgbm.f95, initialization.f95 and !* ldgbm_objfun.f95 as needed. !* !* !* References: !* !* N. Karmitsa, A. Bagirov, "Limited Memory Discrete Gradient Bundle Method !* for Nonsmooth Derivative Free Optimization". Optimization: A Journal of !* Mathematical Programming and Operations Research, Vol. 61, No. 12, !* pp. 1491-1509, 2012. !* !* M.Haarala, K.Miettinen and M.M.Mäkelä: "New Limited Memory !* Bundle Method for Large-Scale Nonsmooth Optimization". !* Optimization Methods and Software 19(6): 673-692, 2004. !* !* N.Haarala, K.Miettinen and M.M.Mäkelä: "Globally Convergent !* Limited Memory Bundle Method for Large-Scale Nonsmooth !* Optimization". Mathematical Programming, Vol. 109, No. 1, !* pp. 181-205, 2007. !* !* !************************************************************************* !* !* * PROGRAM tldgbm * !* !* Main program for limited memory bundle subroutine for large-scale !* unconstrained nonsmooth optimization. !* !************************************************************************* PROGRAM tldgbm USE r_precision, ONLY : prec ! Precision for reals. USE initializat, ONLY : init_x,init_par,mcu,mcinit,n,method ! Initialization of x and parameters. USE exe_time, ONLY : getime ! Execution time. USE ldgbm_mod, ONLY : init_ldgbm,ldgbm ! LDGBM USE lmbm_mod, ONLY : init_lmbm,lmbm ! LMBM USE problem_data, ONLY : next ! Number of the problem ! (remove this when you use your own problem). IMPLICIT NONE ! Scalar Arguments INTEGER :: & mc, & ! Number of corrections. noutit ! Number of outer iterations in LDGBM. REAL(KIND=prec) :: f ! Value of the objective function. ! Array Arguments INTEGER, DIMENSION(4) :: iout ! Output integer parameters. ! iout(1) Number of used iterations. ! iout(2) Number of used function evaluations. ! iout(3) Number of used subgradient evaluations (LMBM) ! or number of outer iterations (LDGBM). ! iout(4) Cause of termination: ! 1 - The problem has been solved ! with desired accuracy. ! 2 - Changes in function values < tolf in mtesf ! subsequent iterations. ! 3 - Changes in function value < ! tolf*small*MAX(|f_k|,|f_(k-1)|,1), ! where small is the smallest positive number ! such that 1.0 + small > 1.0. ! 4 - Number of function calls > mfe. ! 5 - Number of iterations > mit. ! 6 - Time limit exceeded. ! 7 - f < tolb. ! -1 - Two consecutive restarts. ! -2 - Number of restarts > maximum number ! of restarts. ! -3 - Failure in function or subgradient ! calculations (assigned by the user). ! -4 - Failure in attaining the demanded ! accuracy. ! -5 - Invalid input parameters. ! -6 - Unspecified error. ! Local Scalars INTEGER :: i,j REAL :: start,fini DO j=1,10 ! Loop for large-scale nonsmooth test problems in tnsunc ! (remove this if you use your own problem). next=j ! Number of the test problem in tnsunc ! (remove this if you use your own problem). ! Initiation mc = mcinit ! Initial maximum number of stored corrections CALL init_x() CALL init_par() ! CPU-time CALL getime(start) ! Solution IF (method == 2) THEN ! Limited memory discrete gradient bundle method CALL init_ldgbm(mc,iout(4)) ! IF (iout(4) /= 0) STOP 'Something wrong with the initial parameters.' CALL ldgbm(mc,f,iout(3),iout(1),iout(2),iout(4),start) ELSE ! Limited memory bundle method CALL init_lmbm(mc,iout(4)) ! IF (iout(4) /= 0) STOP 'Something wrong with the initial parameters.' CALL lmbm(mc,f,iout(1),iout(2),iout(3),iout(4),start) END IF ! CPU-time CALL getime(fini) ! Result (additional printout, remove ONLY -statement from USE initializat) ! PRINT* ! PRINT*,'next = ',next ! PRINT*,'iterm = ',iout(4) ! PRINT* ! PRINT*,'f(x) = ',f ! PRINT*,'n = ',n ! PRINT*,'na = ',na ! PRINT*,'mcinit = ',mcinit ! PRINT*,'mc = ',mc ! PRINT*,'mcu = ',mcu ! PRINT*,'nit = ',iout(1) ! PRINT*,'nfe = ',iout(2) ! PRINT*,'nge = ',iout(3) ! PRINT*,'xmax = ',xmax ! PRINT*,'gam = ',eta ! PRINT*,'epsl = ',epsl ! PRINT*,'eps = ',tolg ! PRINT*,'method = ',method ! PRINT*,'scaling = ',iscale ! PRINT*,x(1),x(2),x(3),x(4),x(5),x(6),x(7),x(8),x(9),x(10) ! PRINT* ! PRINT*,'Used time = ',fini - start ! PRINT* IF (method == 2) THEN WRITE (6,FMT='(''LDGBM'',I2,I1,1X,''n='',I4,2X, & ''Nout='',I7,1X,''Ni='',I7,1X,''Nf='',I7,1X,''f='',G15.8,2X, & ''Term='',I3,2X,''cpu='',F9.4,2X)') & mcu,mcinit,n,iout(3),iout(1),iout(2),f,iout(4),fini - start ELSE WRITE (6,FMT='(''LMBM'',I2,I1,1X,''n='',I4,2X, & ''Ni='',I7,1X,''Nf='', & I7,1X,''Ng='',I7,1X,''Nfg='',I7,1X,''f='',G15.8,2X, & ''Term='',I3,2X,''cpu='',F9.4,2X)') & mcu,mcinit,n,iout(1),iout(2),iout(3),iout(2)+iout(3) & ,f,iout(4),fini - start END IF PRINT* END DO STOP END PROGRAM tldgbm