callable functions

    function bgo_initialize(T, data, control, status)

Set default control values and initialize private data

Parameters:

data	holds private internal data
control	is a structure containing control information (see bgo_control_type)
status	is a scalar variable of type Int32 that gives the exit status from the package. Possible values are (currently): 0 The initialization was successful.

    function bgo_read_specfile(T, control, specfile)

Read the content of a specification file, and assign values associated with given keywords to the corresponding control parameters. An in-depth discussion of specification files is available, and a detailed list of keywords with associated default values is provided in $GALAHAD/src/bgo/BGO.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/bgo.pdf for a list of how these keywords relate to the components of the control structure. .. rubric:: Parameters:

control	is a structure containing control information (see bgo_control_type)
specfile	is a one-dimensional array of type Vararg{Cchar} that must give the name of the specification file

    function bgo_import(T, control, data, status, n, x_l, x_u,
                        H_type, ne, H_row, H_col, H_ptr)

Import problem data into internal storage prior to solution.

Parameters:

control	is a structure whose members provide control parameters for the remaining procedures (see bgo_control_type)
data	holds private internal data
status	is a scalar variable of type Int32 that gives the exit status from the package. Possible values are: 1 The import was successful, and the package is ready for the solve phase -1 An allocation error occurred. A message indicating the offending array is written on unit control.error, and the returned allocation status and a string containing the name of the offending array are held in inform.alloc_status and inform.bad_alloc respectively. -2 A deallocation error occurred. A message indicating the offending array is written on unit control.error and the returned allocation status and a string containing the name of the offending array are held in inform.alloc_status and inform.bad_alloc respectively. -3 The restriction n > 0 or requirement that type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, ‘diagonal’ or ‘absent’ has been violated.
n	is a scalar variable of type Int32 that holds the number of variables.
x_l	is a one-dimensional array of size n and type T that holds the values \(x^l\) of the lower bounds on the optimization variables \(x\). The j-th component of x_l, \(j = 1, \ldots, n\), contains \(x^l_j\).
x_u	is a one-dimensional array of size n and type T that holds the values \(x^u\) of the upper bounds on the optimization variables \(x\). The j-th component of x_u, \(j = 1, \ldots, n\), contains \(x^u_j\).
H_type	is a one-dimensional array of type Vararg{Cchar} that specifies the symmetric storage scheme used for the Hessian. It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’, ‘diagonal’ or ‘absent’, the latter if access to the Hessian is via matrix-vector products; lower or upper case variants are allowed.
ne	is a scalar variable of type Int32 that holds the number of entries in the lower triangular part of H in the sparse co-ordinate storage scheme. It need not be set for any of the other three schemes.
H_row	is a one-dimensional array of size ne and type Int32 that holds the row indices of the lower triangular part of H in the sparse co-ordinate storage scheme. It need not be set for any of the other three schemes, and in this case can be C_NULL
H_col	is a one-dimensional array of size ne and type Int32 that holds the column indices of the lower triangular part of H in either the sparse co-ordinate, or the sparse row-wise storage scheme. It need not be set when the dense or diagonal storage schemes are used, and in this case can be C_NULL
H_ptr	is a one-dimensional array of size n+1 and type Int32 that holds the starting position of each row of the lower triangular part of H, as well as the total number of entries, in the sparse row-wise storage scheme. It need not be set when the other schemes are used, and in this case can be C_NULL

    function bgo_reset_control(T, control, data, status)

Reset control parameters after import if required.

Parameters:

control	is a structure whose members provide control parameters for the remaining procedures (see bgo_control_type)
data	holds private internal data
status	is a scalar variable of type Int32 that gives the exit status from the package. Possible values are: 1 The import was successful, and the package is ready for the solve phase

    function bgo_solve_with_mat(T, data, userdata, status, n, x, g, ne,
                                eval_f, eval_g, eval_h, eval_hprod, eval_prec)

Find an approximation to the global minimizer of a given function subject to simple bounds on the variables using a multistart trust-region method.

This call is for the case where \(H = \nabla_{xx}f(x)\) is provided specifically, and all function/derivative information is available by function calls.

Parameters:

data	holds private internal data
userdata	is a structure that allows data to be passed into the function and derivative evaluation programs.
status	is a scalar variable of type Int32 that gives the entry and exit status from the package. On initial entry, status must be set to 1. Possible exit values are: 0 The run was successful -1 An allocation error occurred. A message indicating the offending array is written on unit control.error, and the returned allocation status and a string containing the name of the offending array are held in inform.alloc_status and inform.bad_alloc respectively. -2 A deallocation error occurred. A message indicating the offending array is written on unit control.error and the returned allocation status and a string containing the name of the offending array are held in inform.alloc_status and inform.bad_alloc respectively. -3 The restriction n > 0 or requirement that type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, ‘diagonal’ or ‘absent’ has been violated. -7 The objective function appears to be unbounded from below -9 The analysis phase of the factorization failed; the return status from the factorization package is given in the component inform.factor_status -10 The factorization failed; the return status from the factorization package is given in the component inform.factor_status. -11 The solution of a set of linear equations using factors from the factorization package failed; the return status from the factorization package is given in the component inform.factor_status. -16 The problem is so ill-conditioned that further progress is impossible. -18 Too many iterations have been performed. This may happen if control.maxit is too small, but may also be symptomatic of a badly scaled problem. -19 The CPU time limit has been reached. This may happen if control.cpu_time_limit is too small, but may also be symptomatic of a badly scaled problem. -82 The user has forced termination of solver by removing the file named control.alive_file from unit unit control.alive_unit.
n	is a scalar variable of type Int32 that holds the number of variables
x	is a one-dimensional array of size n and type T that holds the values \(x\) of the optimization variables. The j-th component of x, j = 1, … , n, contains \(x_j\).
g	is a one-dimensional array of size n and type T that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 1, … , n, contains \(g_j\).
ne	is a scalar variable of type Int32 that holds the number of entries in the lower triangular part of the Hessian matrix \(H\).
eval_f	is a user-supplied function that must have the following signature: function eval_f(n, x, f, userdata) The value of the objective function \(f(x)\) evaluated at x=\(x\) must be assigned to f, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_f via the structure userdata.
eval_g	is a user-supplied function that must have the following signature: function eval_g(n, x, g, userdata) The components of the gradient \(g = \nabla_x f(x\)) of the objective function evaluated at x=\(x\) must be assigned to g, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_g via the structure userdata.
eval_h	is a user-supplied function that must have the following signature: function eval_h(n, ne, x, h, userdata) The nonzeros of the Hessian \(H = \nabla_{xx}f(x)\) of the objective function evaluated at x=\(x\) must be assigned to h in the same order as presented to bgo_import, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_h via the structure userdata.
eval_prec	is an optional user-supplied function that may be C_NULL. If non-NULL, it must have the following signature: function eval_prec(n, x, u, v, userdata) The product \(u = P(x) v\) of the user’s preconditioner \(P(x)\) evaluated at \(x\) with the vector v=\(v\), the result \(u\) must be retured in u, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_prec via the structure userdata.

    function bgo_solve_without_mat(T, data, userdata, status, n, x, g,
                                   eval_f, eval_g, eval_hprod,
                                   eval_shprod, eval_prec)

Find an approximation to the global minimizer of a given function subject to simple bounds on the variables using a multistart trust-region method.

This call is for the case where access to \(H = \nabla_{xx}f(x)\) is provided by Hessian-vector products, and all function/derivative information is available by function calls.

Parameters:

data	holds private internal data
userdata	is a structure that allows data to be passed into the function and derivative evaluation programs.
status	is a scalar variable of type Int32 that gives the entry and exit status from the package. On initial entry, status must be set to 1. Possible exit values are: 0 The run was successful -1 An allocation error occurred. A message indicating the offending array is written on unit control.error, and the returned allocation status and a string containing the name of the offending array are held in inform.alloc_status and inform.bad_alloc respectively. -2 A deallocation error occurred. A message indicating the offending array is written on unit control.error and the returned allocation status and a string containing the name of the offending array are held in inform.alloc_status and inform.bad_alloc respectively. -3 The restriction n > 0 or requirement that type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, ‘diagonal’ or ‘absent’ has been violated. -7 The objective function appears to be unbounded from below -9 The analysis phase of the factorization failed; the return status from the factorization package is given in the component inform.factor_status -10 The factorization failed; the return status from the factorization package is given in the component inform.factor_status. -11 The solution of a set of linear equations using factors from the factorization package failed; the return status from the factorization package is given in the component inform.factor_status. -16 The problem is so ill-conditioned that further progress is impossible. -18 Too many iterations have been performed. This may happen if control.maxit is too small, but may also be symptomatic of a badly scaled problem. -19 The CPU time limit has been reached. This may happen if control.cpu_time_limit is too small, but may also be symptomatic of a badly scaled problem. -82 The user has forced termination of solver by removing the file named control.alive_file from unit unit control.alive_unit.
n	is a scalar variable of type Int32 that holds the number of variables
x	is a one-dimensional array of size n and type T that holds the values \(x\) of the optimization variables. The j-th component of x, j = 1, … , n, contains \(x_j\).
g	is a one-dimensional array of size n and type T that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 1, … , n, contains \(g_j\).
eval_f	is a user-supplied function that must have the following signature: function eval_f(n, x, f, userdata) The value of the objective function \(f(x)\) evaluated at x=\(x\) must be assigned to f, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_f via the structure userdata.
eval_g	is a user-supplied function that must have the following signature: function eval_g(n, x, g, userdata) The components of the gradient \(g = \nabla_x f(x\)) of the objective function evaluated at x=\(x\) must be assigned to g, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_g via the structure userdata.
eval_hprod	is a user-supplied function that must have the following signature: function eval_hprod(n, x, u, v, got_h, userdata) The sum \(u + \nabla_{xx}f(x) v\) of the product of the Hessian \(\nabla_{xx}f(x)\) of the objective function evaluated at x=\(x\) with the vector v=\(v\) and the vector $ \(u\) must be returned in u, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. The Hessian has already been evaluated or used at x if the Bool got_h is true. Data may be passed into eval_hprod via the structure userdata.
eval_shprod	is a user-supplied function that must have the following signature: function eval_shprod(n, x, nnz_v, index_nz_v, v, nnz_u, index_nz_u, u, got_h, userdata) The product \(u = \nabla_{xx}f(x) v\) of the Hessian \(\nabla_{xx}f(x)\) of the objective function evaluated at \(x\) with the sparse vector v=\(v\) must be returned in u, and the function return value set to 0. Only the components index_nz_v[0:nnz_v-1] of v are nonzero, and the remaining components may not have been be set. On exit, the user must indicate the nnz_u indices of u that are nonzero in index_nz_u[0:nnz_u-1], and only these components of u need be set. If the evaluation is impossible at x, return should be set to a nonzero value. The Hessian has already been evaluated or used at x if the Bool got_h is true. Data may be passed into eval_prec via the structure userdata.
eval_prec	is an optional user-supplied function that may be C_NULL. If non-NULL, it must have the following signature: function eval_prec(n, x, u, v, userdata) The product \(u = P(x) v\) of the user’s preconditioner \(P(x)\) evaluated at \(x\) with the vector v=\(v\), the result \(u\) must be retured in u, and the function return value set to 0. If the evaluation is impossible at x, return should be set to a nonzero value. Data may be passed into eval_prec via the structure userdata.

    function bgo_solve_reverse_with_mat(T, data, status, eval_status,
                                        n, x, f, g, ne, H_val, u, v)

Find an approximation to the global minimizer of a given function subject to simple bounds on the variables using a multistart trust-region method.

This call is for the case where \(H = \nabla_{xx}f(x)\) is provided specifically, but function/derivative information is only available by returning to the calling procedure

Parameters:

data	holds private internal data
status	is a scalar variable of type Int32 that gives the entry and exit status from the package. On initial entry, status must be set to 1. Possible exit values are: 0 The run was successful -1 An allocation error occurred. A message indicating the offending array is written on unit control.error, and the returned allocation status and a string containing the name of the offending array are held in inform.alloc_status and inform.bad_alloc respectively. -2 A deallocation error occurred. A message indicating the offending array is written on unit control.error and the returned allocation status and a string containing the name of the offending array are held in inform.alloc_status and inform.bad_alloc respectively. -3 The restriction n > 0 or requirement that type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, ‘diagonal’ or ‘absent’ has been violated. -7 The objective function appears to be unbounded from below -9 The analysis phase of the factorization failed; the return status from the factorization package is given in the component inform.factor_status -10 The factorization failed; the return status from the factorization package is given in the component inform.factor_status. -11 The solution of a set of linear equations using factors from the factorization package failed; the return status from the factorization package is given in the component inform.factor_status. -16 The problem is so ill-conditioned that further progress is impossible. -18 Too many iterations have been performed. This may happen if control.maxit is too small, but may also be symptomatic of a badly scaled problem. -19 The CPU time limit has been reached. This may happen if control.cpu_time_limit is too small, but may also be symptomatic of a badly scaled problem. -82 The user has forced termination of solver by removing the file named control.alive_file from unit unit control.alive_unit. 2 The user should compute the objective function value \(f(x)\) at the point \(x\) indicated in x and then re-enter the function. The required value should be set in f, and eval_status should be set to 0. If the user is unable to evaluate \(f(x)\) for instance, if the function is undefined at \(x\) the user need not set f, but should then set eval_status to a non-zero value. 3 The user should compute the gradient of the objective function \(\nabla_x f(x)\) at the point \(x\) indicated in x and then re-enter the function. The value of the i-th component of the gradient should be set in g[i], for i = 1, …, n and eval_status should be set to 0. If the user is unable to evaluate a component of \(\nabla_x f(x)\) for instance if a component of the gradient is undefined at \(x\) -the user need not set g, but should then set eval_status to a non-zero value. 4 The user should compute the Hessian of the objective function \(\nabla_{xx}f(x)\) at the point x indicated in \(x\) and then re-enter the function. The value l-th component of the Hessian stored according to the scheme input in the remainder of \(H\) should be set in H_val[l], for l = 0, …, ne-1 and eval_status should be set to 0. If the user is unable to evaluate a component of \(\nabla_{xx}f(x)\) for instance, if a component of the Hessian is undefined at \(x\) the user need not set H_val, but should then set eval_status to a non-zero value. 5 The user should compute the product \(\nabla_{xx}f(x)v\) of the Hessian of the objective function \(\nabla_{xx}f(x)\) at the point \(x\) indicated in x with the vector \(v\), add the result to the vector \(u\) and then re-enter the function. The vectors \(u\) and \(v\) are given in u and v respectively, the resulting vector \(u + \nabla_{xx}f(x)v\) should be set in u and eval_status should be set to 0. If the user is unable to evaluate the product for instance, if a component of the Hessian is undefined at \(x\) the user need not alter u, but should then set eval_status to a non-zero value. 6 The user should compute the product \(u = P(x)v\) of their preconditioner \(P(x)\) at the point x indicated in \(x\) with the vector \(v\) and then re-enter the function. The vector \(v\) is given in v, the resulting vector \(u = P(x)v\) should be set in u and eval_status should be set to 0. If the user is unable to evaluate the product for instance, if a component of the preconditioner is undefined at \(x\) the user need not set u, but should then set eval_status to a non-zero value. 23 The user should follow the instructions for 2 and 3 above before returning. 25 The user should follow the instructions for 2 and 5 above before returning. 35 The user should follow the instructions for 3 and 5 above before returning. 235 The user should follow the instructions for 2, 3 and 5 above before returning.
eval_status	is a scalar variable of type Int32 that is used to indicate if objective function/gradient/Hessian values can be provided (see above)
n	is a scalar variable of type Int32 that holds the number of variables
x	is a one-dimensional array of size n and type T that holds the values \(x\) of the optimization variables. The j-th component of x, j = 1, … , n, contains \(x_j\).
f	is a scalar variable pointer of type T that holds the value of the objective function.
g	is a one-dimensional array of size n and type T that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 1, … , n, contains \(g_j\).
ne	is a scalar variable of type Int32 that holds the number of entries in the lower triangular part of the Hessian matrix \(H\).
H_val	is a one-dimensional array of size ne and type T that holds the values of the entries of the lower triangular part of the Hessian matrix \(H\) in any of the available storage schemes.
u	is a one-dimensional array of size n and type T that is used for reverse communication (see above for details)
v	is a one-dimensional array of size n and type T that is used for reverse communication (see above for details)

    function bgo_solve_reverse_without_mat(T, data, status, eval_status,
                                            n, x, f, g, u, v, index_nz_v,
                                            nnz_v, index_nz_u, nnz_u)

Find an approximation to the global minimizer of a given function subject to simple bounds on the variables using a multistart trust-region method.

This call is for the case where access to \(H = \nabla_{xx}f(x)\) is provided by Hessian-vector products, but function/derivative information is only available by returning to the calling procedure.

Parameters:

data	holds private internal data
status	is a scalar variable of type Int32 that gives the entry and exit status from the package. On initial entry, status must be set to 1. Possible exit values are: 0 The run was successful -1 An allocation error occurred. A message indicating the offending array is written on unit control.error, and the returned allocation status and a string containing the name of the offending array are held in inform.alloc_status and inform.bad_alloc respectively. -2 A deallocation error occurred. A message indicating the offending array is written on unit control.error and the returned allocation status and a string containing the name of the offending array are held in inform.alloc_status and inform.bad_alloc respectively. -3 The restriction n > 0 or requirement that type contains its relevant string ‘dense’, ‘coordinate’, ‘sparse_by_rows’, ‘diagonal’ or ‘absent’ has been violated. -7 The objective function appears to be unbounded from below -9 The analysis phase of the factorization failed; the return status from the factorization package is given in the component inform.factor_status -10 The factorization failed; the return status from the factorization package is given in the component inform.factor_status. -11 The solution of a set of linear equations using factors from the factorization package failed; the return status from the factorization package is given in the component inform.factor_status. -16 The problem is so ill-conditioned that further progress is impossible. -18 Too many iterations have been performed. This may happen if control.maxit is too small, but may also be symptomatic of a badly scaled problem. -19 The CPU time limit has been reached. This may happen if control.cpu_time_limit is too small, but may also be symptomatic of a badly scaled problem. -82 The user has forced termination of solver by removing the file named control.alive_file from unit unit control.alive_unit. 2 The user should compute the objective function value \(f(x)\) at the point \(x\) indicated in x and then re-enter the function. The required value should be set in f, and eval_status should be set to 0. If the user is unable to evaluate \(f(x)\) for instance, if the function is undefined at \(x\) the user need not set f, but should then set eval_status to a non-zero value. 3 The user should compute the gradient of the objective function \(\nabla_x f(x)\) at the point \(x\) indicated in x and then re-enter the function. The value of the i-th component of the gradient should be set in g[i], for i = 1, …, n and eval_status should be set to 0. If the user is unable to evaluate a component of \(\nabla_x f(x)\) for instance if a component of the gradient is undefined at \(x\) -the user need not set g, but should then set eval_status to a non-zero value. 5 The user should compute the product \(\nabla_{xx}f(x)v\) of the Hessian of the objective function \(\nabla_{xx}f(x)\) at the point \(x\) indicated in x with the vector \(v\), add the result to the vector \(u\) and then re-enter the function. The vectors \(u\) and \(v\) are given in u and v respectively, the resulting vector \(u + \nabla_{xx}f(x)v\) should be set in u and eval_status should be set to 0. If the user is unable to evaluate the product for instance, if a component of the Hessian is undefined at \(x\) the user need not alter u, but should then set eval_status to a non-zero value. 6 The user should compute the product \(u = P(x)v\) of their preconditioner \(P(x)\) at the point x indicated in \(x\) with the vector \(v\) and then re-enter the function. The vector \(v\) is given in v, the resulting vector \(u = P(x)v\) should be set in u and eval_status should be set to 0. If the user is unable to evaluate the product for instance, if a component of the preconditioner is undefined at \(x\) the user need not set u, but should then set eval_status to a non-zero value. 7 The user should compute the product \(u = \nabla_{xx}f(x)v\) of the Hessian of the objective function \(\nabla_{xx}f(x)\) at the point \(x\) indicated in x with the sparse vector v=\(v\) and then re-enter the function. The nonzeros of \(v\) are stored in v[index_nz_v[0:nnz_v-1]] while the nonzeros of \(u\) should be returned in u[index_nz_u[0:nnz_u-1]]; the user must set nnz_u and index_nz_u accordingly, and set eval_status to 0. If the user is unable to evaluate the product for instance, if a component of the Hessian is undefined at \(x\) the user need not alter u, but should then set eval_status to a non-zero value. 23 The user should follow the instructions for 2 and 3 above before returning. 25 The user should follow the instructions for 2 and 5 above before returning. 35 The user should follow the instructions for 3 and 5 above before returning. 235 The user should follow the instructions for 2, 3 and 5 above before returning.
eval_status	is a scalar variable of type Int32 that is used to indicate if objective function/gradient/Hessian values can be provided (see above)
n	is a scalar variable of type Int32 that holds the number of variables
x	is a one-dimensional array of size n and type T that holds the values \(x\) of the optimization variables. The j-th component of x, j = 1, … , n, contains \(x_j\).
f	is a scalar variable pointer of type T that holds the value of the objective function.
g	is a one-dimensional array of size n and type T that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 1, … , n, contains \(g_j\).
u	is a one-dimensional array of size n and type T that is used for reverse communication (see status=5,6,7 above for details)
v	is a one-dimensional array of size n and type T that is used for reverse communication (see status=5,6,7 above for details)
index_nz_v	is a one-dimensional array of size n and type Int32 that is used for reverse communication (see status=7 above for details)
nnz_v	is a scalar variable of type Int32 that is used for reverse communication (see status=7 above for details)
index_nz_u	is a one-dimensional array of size n and type Int32 that is used for reverse communication (see status=7 above for details)
nnz_u	is a scalar variable of type Int32 that is used for reverse communication (see status=7 above for details). On initial (status=1) entry, nnz_u should be set to an (arbitrary) nonzero value, and nnz_u=0 is recommended

    function bgo_information(T, data, inform, status)

Provides output information

Parameters:

data	holds private internal data
inform	is a structure containing output information (see bgo_inform_type)
status	is a scalar variable of type Int32 that gives the exit status from the package. Possible values are (currently): 0 The values were recorded successfully

    function bgo_terminate(T, data, control, inform)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a structure containing control information (see bgo_control_type)
inform	is a structure containing output information (see bgo_inform_type)