The main routine.
This subroutine partitions the working arrays wa and iwa, and
then uses the limited memory BFGS method to solve the bound
constrained optimization problem by calling mainlb.
(The direct method will be used in the subspace minimization.)
| Type | Intent | Optional | Attributes | Name | ||
|---|---|---|---|---|---|---|
| integer, | intent(in) | :: | n |
the dimension of the problem (the number of variables). |
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| integer, | intent(in) | :: | m |
the maximum number of variable metric corrections
used to define the limited memory matrix.
Values of |
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| real(kind=wp), | intent(inout) | :: | x(n) |
On initial entry it must be set by the user to the values of the initial estimate of the solution vector. Upon successful exit, it contains the values of the variables at the best point found (usually an approximate solution). |
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| real(kind=wp), | intent(in) | :: | l(n) |
the lower bound on |
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| real(kind=wp), | intent(in) | :: | u(n) |
the upper bound on |
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| integer, | intent(in) | :: | Nbd(n) |
nbd represents the type of bounds imposed on the variables, and must be specified as follows:
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| real(kind=wp), | intent(inout) | :: | f |
On first entry |
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| real(kind=wp), | intent(inout) | :: | g(n) |
On first entry |
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| real(kind=wp), | intent(in) | :: | Factr |
A tolerance in the termination test for the algorithm. The iteration will stop when:
where
The user can suppress this termination test by setting |
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| real(kind=wp), | intent(in) | :: | Pgtol |
The iteration will stop when:
where |
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| real(kind=wp) | :: | Wa(2*m*n+5*n+11*m*m+8*m) |
working array of length |
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| integer | :: | Iwa(3*n) |
an integer working array of length |
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| character(len=60), | intent(inout) | :: | Task |
Indicates the current job when entering and quitting this subroutine:
On exit with task = 'CONV', 'ABNO' or 'ERROR', the variable task contains additional information that the user can print. This array should not be altered unless the user wants to stop the run for some reason. See driver2 or driver3 for a detailed explanation on how to stop the run by assigning task(1:4)='STOP' in the driver. |
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| integer, | intent(in) | :: | Iprint |
Controls the frequency and type of output generated:
When |
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| character(len=60) | :: | Csave |
working string |
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| logical | :: | Lsave(4) |
A logical working array of dimension 4.
On exit with
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| integer | :: | Isave(44) |
An integer working array of dimension 44. On exit with 'task' = NEW_X, the following information is available:
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| real(kind=wp) | :: | Dsave(29) |
A real(wp) working array of dimension 29. On exit with 'task' = NEW_X, the following information is available:
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| character(len=*), | intent(in), | optional | :: | iteration_file |
The name of the iteration file if used ( |
subroutine setulb(n,m,x,l,u,Nbd,f,g,Factr,Pgtol,Wa,Iwa,Task, & Iprint,Csave,Lsave,Isave,Dsave,iteration_file) implicit none integer,intent(in) :: n !! the dimension of the problem (the number of variables). integer,intent(in) :: m !! the maximum number of variable metric corrections !! used to define the limited memory matrix. !! Values of `m < 3` are !! not recommended, and large values of `m` can result in excessive !! computing time. The range `3 <= m <= 20` is recommended. real(wp),intent(inout) :: x(n) !! On initial entry !! it must be set by the user to the values of the initial !! estimate of the solution vector. Upon successful exit, it !! contains the values of the variables at the best point !! found (usually an approximate solution). real(wp),intent(in) :: l(n) !! the lower bound on `x`. If !! the `i`-th variable has no lower bound, !! `l(i)` need not be defined. real(wp),intent(in) :: u(n) !! the upper bound on `x`. If !! the `i`-th variable has no upper bound, !! `u(i)` need not be defined. integer,intent(in) :: Nbd(n) !! nbd represents the type of bounds imposed on the !! variables, and must be specified as follows: !! !! * `nbd(i)=0` if `x(i)` is unbounded !! * `nbd(i)=1` if `x(i)` has only a lower bound !! * `nbd(i)=2` if `x(i)` has both lower and upper bounds !! * `nbd(i)=3` if `x(i)` has only an upper bound real(wp),intent(inout) :: f !! On first entry `f` is unspecified. !! On final exit `f` is the value of the function at x. !! If the [[setulb]] returns !! with `task(1:2)= 'FG'`, then `f` must be set by the user to !! contain the value of the function at the point `x`. real(wp),intent(inout) :: g(n) !! On first entry `g` is unspecified. !! On final exit `g` is the value of the gradient at `x`. !! If the [[setulb]] !! returns with `task(1:2)= 'FG'`, then `g` must be set by the user to !! contain the components of the gradient at the point `x`. real(wp),intent(in) :: Factr !! A tolerance in the termination test for the algorithm. !! The iteration will stop when: !! !! `(f^k - f^{k+1})/max{|f^k|,|f^{k+1}|,1} <= factr*epsmch` !! !! where `epsmch` is the machine precision. !! Typical values for `factr` on a computer !! with 15 digits of accuracy in real(wp) are: !! !! * `factr=1.0e+12` for low accuracy !! * `factr=1.0e+7` for moderate accuracy !! * `factr=1.0e+1` for extremely high accuracy !! !! The user can suppress this termination test by setting `factr=0`. real(wp),intent(in) :: Pgtol !! The iteration will stop when: !! !! `max{|proj g_i | i = 1, ..., n} <= pgtol` !! !! where `pg_i` is the `i`th component of the projected gradient. !! The user can suppress this termination test by setting `pgtol=0`. real(wp) :: Wa(2*m*n+5*n+11*m*m+8*m) !! working array of length `(2mmax + 5)nmax + 11mmax^2 + 8mmax`. !! This array must not be altered by the user. integer :: Iwa(3*n) !! an integer working array of length `3nmax`. !! This array must not be altered by the user. character(len=60),intent(inout) :: Task !! Indicates the current job when entering and quitting this subroutine: !! !! * On first entry, it must be set to 'START'. !! * On a return with task(1:2)='FG', the user must evaluate the !! function f and gradient g at the returned value of x. !! * On a return with task(1:5)='NEW_X', an iteration of the !! algorithm has concluded, and f and g contain f(x) and g(x) !! respectively. The user can decide whether to continue or stop !! the iteration. !! * When task(1:4)='CONV', the termination test in L-BFGS-B has been !! satisfied; !! * When task(1:4)='ABNO', the routine has terminated abnormally !! without being able to satisfy the termination conditions, !! x contains the best approximation found, !! f and g contain f(x) and g(x) respectively; !! * When task(1:5)='ERROR', the routine has detected an error in the !! input parameters; !! !! On exit with task = 'CONV', 'ABNO' or 'ERROR', the variable task !! contains additional information that the user can print. !! !! This array should not be altered unless the user wants to !! stop the run for some reason. See driver2 or driver3 !! for a detailed explanation on how to stop the run !! by assigning task(1:4)='STOP' in the driver. integer,intent(in) :: Iprint !! Controls the frequency and type of output generated: !! !! * `iprint<0 ` no output is generated !! * `iprint=0 ` print only one line at the last iteration !! * `0<iprint<99` print also `f` and `|proj g|` every `iprint` iterations !! * `iprint=99 ` print details of every iteration except `n`-vectors !! * `iprint=100 ` print also the changes of active set and final `x` !! * `iprint>100 ` print details of every iteration including `x` and `g` !! !! When `iprint > 0`, the file `iterate.dat` will be created to !! summarize the iteration. character(len=60) :: Csave !! working string logical :: Lsave(4) !! A logical working array of dimension 4. !! On exit with `task = 'NEW_X'`, the following information is available: !! !! * If `lsave(1) = .true.` then the initial `x` did not satisfy the bounds !! and `x` has been replaced by its projection in the feasible set !! * If `lsave(2) = .true.` then the problem is constrained !! * If `lsave(3) = .true.` then each variable has upper and lower bounds integer :: Isave(44) !! An integer working array of dimension 44. !! On exit with 'task' = NEW_X, the following information is available: !! !! * isave(22) = the total number of intervals explored in the !! search of Cauchy points; !! * isave(26) = the total number of skipped BFGS updates before !! the current iteration; !! * isave(30) = the number of current iteration; !! * isave(31) = the total number of BFGS updates prior the current !! iteration; !! * isave(33) = the number of intervals explored in the search of !! Cauchy point in the current iteration; !! * isave(34) = the total number of function and gradient !! evaluations; !! * isave(36) = the number of function value or gradient !! evaluations in the current iteration; !! * if isave(37) = 0 then the subspace argmin is within the box; !! * if isave(37) = 1 then the subspace argmin is beyond the box; !! * isave(38) = the number of free variables in the current !! iteration; !! * isave(39) = the number of active constraints in the current !! iteration; !! * n + 1 - isave(40) = the number of variables leaving the set of !! active constraints in the current iteration; !! * isave(41) = the number of variables entering the set of active !! constraints in the current iteration. real(wp) :: Dsave(29) !! A real(wp) working array of dimension 29. !! On exit with 'task' = NEW_X, the following information is available: !! !! * dsave(1) = current 'theta' in the BFGS matrix; !! * dsave(2) = f(x) in the previous iteration; !! * dsave(3) = factr*epsmch; !! * dsave(4) = 2-norm of the line search direction vector; !! * dsave(5) = the machine precision epsmch generated by the code; !! * dsave(7) = the accumulated time spent on searching for !! Cauchy points; !! * dsave(8) = the accumulated time spent on !! subspace minimization; !! * dsave(9) = the accumulated time spent on line search; !! * dsave(11) = the slope of the line search function at !! the current point of line search; !! * dsave(12) = the maximum relative step length imposed in !! line search; !! * dsave(13) = the infinity norm of the projected gradient; !! * dsave(14) = the relative step length in the line search; !! * dsave(15) = the slope of the line search function at !! the starting point of the line search; !! * dsave(16) = the square of the 2-norm of the line search !! direction vector. character(len=*),intent(in),optional :: iteration_file !! The name of the iteration file if used (`Iprint>=1`). !! If not specified, then 'iterate.dat' is used. integer :: lws , lr , lz , lt , ld , lxp , lwa , lwy , lsy , lss , & lwt , lwn , lsnd if ( Task=='START' ) then Isave(1) = m*n Isave(2) = m**2 Isave(3) = 4*m**2 Isave(4) = 1 ! ws m*n Isave(5) = Isave(4) + Isave(1) ! wy m*n Isave(6) = Isave(5) + Isave(1) ! wsy m**2 Isave(7) = Isave(6) + Isave(2) ! wss m**2 Isave(8) = Isave(7) + Isave(2) ! wt m**2 Isave(9) = Isave(8) + Isave(2) ! wn 4*m**2 Isave(10) = Isave(9) + Isave(3) ! wsnd 4*m**2 Isave(11) = Isave(10) + Isave(3) ! wz n Isave(12) = Isave(11) + n ! wr n Isave(13) = Isave(12) + n ! wd n Isave(14) = Isave(13) + n ! wt n Isave(15) = Isave(14) + n ! wxp n Isave(16) = Isave(15) + n ! wa 8*m endif lws = Isave(4) lwy = Isave(5) lsy = Isave(6) lss = Isave(7) lwt = Isave(8) lwn = Isave(9) lsnd = Isave(10) lz = Isave(11) lr = Isave(12) ld = Isave(13) lt = Isave(14) lxp = Isave(15) lwa = Isave(16) call mainlb(n,m,x,l,u,Nbd,f,g,Factr,Pgtol,Wa(lws),Wa(lwy),Wa(lsy),& Wa(lss),Wa(lwt),Wa(lwn),Wa(lsnd),Wa(lz),Wa(lr),Wa(ld),& Wa(lt),Wa(lxp),Wa(lwa),Iwa(1),Iwa(n+1),Iwa(2*n+1), & Task,Iprint,Csave,Lsave,Isave(22),Dsave,iteration_file) end subroutine setulb