overview of functions provided

// typedefs

typedef float spc_;
typedef double rpc_;
typedef int ipc_;

// structs

struct dgo_control_type;
struct dgo_inform_type;
struct dgo_time_type;

// function calls

void dgo_initialize(void **data, struct dgo_control_type* control, ipc_ *status);
void dgo_read_specfile(struct dgo_control_type* control, const char specfile[]);

void dgo_import(
    struct dgo_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    const rpc_ x_l[],
    const rpc_ x_u[],
    const char H_type[],
    ipc_ ne,
    const ipc_ H_row[],
    const ipc_ H_col[],
    const ipc_ H_ptr[]
);

void dgo_reset_control(
    struct dgo_control_type* control,
    void **data,
    ipc_ *status
);

void dgo_solve_with_mat(
    void **data,
    void *userdata,
    ipc_ *status,
    ipc_ n,
    rpc_ x[],
    rpc_ g[],
    ipc_ ne,
    ipc_(*)(ipc_, const rpc_[], rpc_*, const void*) eval_f,
    ipc_(*)(ipc_, const rpc_[], rpc_[], const void*) eval_g,
    ipc_(*)(ipc_, ipc_, const rpc_[], rpc_[], const void*) eval_h,
    ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], bool, const void*) eval_hprod,
    ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], const void*) eval_prec
);

void dgo_solve_without_mat(
    void **data,
    void *userdata,
    ipc_ *status,
    ipc_ n,
    rpc_ x[],
    rpc_ g[],
    ipc_(*)(ipc_, const rpc_[], rpc_*, const void*) eval_f,
    ipc_(*)(ipc_, const rpc_[], rpc_[], const void*) eval_g,
    ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], bool, const void*) eval_hprod,
    ipc_(*)(ipc_, const rpc_[], ipc_, const int[], const rpc_[], int*, int[], rpc_[], bool, const void*) eval_shprod,
    ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], const void*) eval_prec
);

void dgo_solve_reverse_with_mat(
    void **data,
    ipc_ *status,
    ipc_ *eval_status,
    ipc_ n,
    rpc_ x[],
    rpc_ f,
    rpc_ g[],
    ipc_ ne,
    rpc_ H_val[],
    const rpc_ u[],
    rpc_ v[]
);

void dgo_solve_reverse_without_mat(
    void **data,
    ipc_ *status,
    ipc_ *eval_status,
    ipc_ n,
    rpc_ x[],
    rpc_ f,
    rpc_ g[],
    rpc_ u[],
    rpc_ v[],
    ipc_ index_nz_v[],
    ipc_ *nnz_v,
    const ipc_ index_nz_u[],
    ipc_ nnz_u
);

void dgo_information(void **data, struct dgo_inform_type* inform, ipc_ *status);

void dgo_terminate(
    void **data,
    struct dgo_control_type* control,
    struct dgo_inform_type* inform
);

typedefs

typedef float spc_

spc_ is real single precision

typedef double rpc_

rpc_ is the real working precision used, but may be changed to float by defining the preprocessor variable REAL_32 or (if supported) to __real128 using the variable REAL_128.

typedef int ipc_

ipc_ is the default integer word length used, but may be changed to int64_t by defining the preprocessor variable INTEGER_64.

function and structure names

The function and structure names described below are appropriate for the default real working precision (double) and integer word length (int32_t). To use the functions and structures with different precisions and integer word lengths, an additional suffix must be added to their names (and the arguments set accordingly). The appropriate suffices are:

_s for single precision (float) reals and standard 32-bit (int32_t) integers;

_q for quadruple precision (__real128) reals (if supported) and standard 32-bit (int32_t) integers;

_64 for standard precision (double) reals and 64-bit (int64_t) integers;

_s_64 for single precision (float) reals and 64-bit (int64_t) integers; and

_q_64 for quadruple precision (__real128) reals (if supported) and 64-bit (int64_t) integers.

Thus a call to dgo_initialize below will instead be

void dgo_initialize_s_64(void **data, struct dgo_control_type_s_64* control,
                         int64_t *status)

if single precision (float) reals and 64-bit (int64_t) integers are required. Thus it is possible to call functions for this package with more that one precision and/or integer word length at same time. An example is provided for the package expo, and the obvious modifications apply equally here.

function calls

void dgo_initialize(void **data, struct dgo_control_type* control, ipc_ *status)

Set default control values and initialize private data

Parameters:

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

void dgo_read_specfile(struct dgo_control_type* control, const char 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/dgo/DGO.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/dgo.pdf for a list of how these keywords relate to the components of the control structure.

Parameters:

control	is a struct containing control information (see dgo_control_type)
specfile	is a character string containing the name of the specification file

void dgo_import(
    struct dgo_control_type* control,
    void **data,
    ipc_ *status,
    ipc_ n,
    const rpc_ x_l[],
    const rpc_ x_u[],
    const char H_type[],
    ipc_ ne,
    const ipc_ H_row[],
    const ipc_ H_col[],
    const ipc_ H_ptr[]
)

Import problem data into internal storage prior to solution.

Parameters:

control	is a struct whose members provide control paramters for the remaining prcedures (see dgo_control_type)
data	holds private internal data
status	is a scalar variable of type ipc_, 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 ipc_, that holds the number of variables.
x_l	is a one-dimensional array of size n and type rpc_, that holds the values \(x^l\) of the lower bounds on the optimization variables \(x\). The j-th component of x_l, \(j = 0, \ldots, n-1\), contains \(x^l_j\).
x_u	is a one-dimensional array of size n and type rpc_, that holds the values \(x^u\) of the upper bounds on the optimization variables \(x\). The j-th component of x_u, \(j = 0, \ldots, n-1\), contains \(x^u_j\).
H_type	is a one-dimensional array of type char 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 ipc_, 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 ipc_, 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 NULL
H_col	is a one-dimensional array of size ne and type ipc_, 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 NULL
H_ptr	is a one-dimensional array of size n+1 and type ipc_, 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 NULL

void dgo_reset_control(
    struct dgo_control_type* control,
    void **data,
    ipc_ *status
)

Reset control parameters after import if required.

Parameters:

control	is a struct whose members provide control paramters for the remaining prcedures (see dgo_control_type)
data	holds private internal data
status	is a scalar variable of type ipc_, that gives the exit status from the package. Possible values are: The import was successful, and the package is ready for the solve phase

void dgo_solve_with_mat(
    void **data,
    void *userdata,
    ipc_ *status,
    ipc_ n,
    rpc_ x[],
    rpc_ g[],
    ipc_ ne,
    ipc_(*)(ipc_, const rpc_[], rpc_*, const void*) eval_f,
    ipc_(*)(ipc_, const rpc_[], rpc_[], const void*) eval_g,
    ipc_(*)(ipc_, ipc_, const rpc_[], rpc_[], const void*) eval_h,
    ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], bool, const void*) eval_hprod,
    ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], const void*) eval_prec
)

Find an approximation to the global minimizer of a given function subject to simple bounds on the variables using a partition-and-bound 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 ipc_, 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. -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. -91 The hash table used to store the dictionary of vertices of the sub-boxes is full, and there is no room to increase it further. -99 The budget limit on function evaluations has been reached. This will happen if the limit control.max_evals is exceeded, and is quite normal for stochastic global-optimization methods. The user may explore increasing control.max_evals to see if that produces a lower value of the objective function, but there are unfortunately no guarantees.
n	is a scalar variable of type ipc_, that holds the number of variables
x	is a one-dimensional array of size n and type rpc_, that holds the values \(x\) of the optimization variables. The j-th component of x, j = 0, … , n-1, contains \(x_j\).
g	is a one-dimensional array of size n and type rpc_, that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 0, … , n-1, contains \(g_j\).
ne	is a scalar variable of type ipc_, 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: ipc_ eval_f( ipc_ n, const rpc_ x[], rpc_ *f, const void *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: ipc_ eval_g( ipc_ n, const rpc_ x[], rpc_ g[], const void *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: ipc_ eval_h( ipc_ n, ipc_ ne, const rpc_ x[], rpc_ h[], const void *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 dgo_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 NULL. If non-NULL, it must have the following signature: ipc_ eval_prec( ipc_ n, const rpc_ x[], rpc_ u[], const rpc_ v[], const void *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.

void dgo_solve_without_mat(
    void **data,
    void *userdata,
    ipc_ *status,
    ipc_ n,
    rpc_ x[],
    rpc_ g[],
    ipc_(*)(ipc_, const rpc_[], rpc_*, const void*) eval_f,
    ipc_(*)(ipc_, const rpc_[], rpc_[], const void*) eval_g,
    ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], bool, const void*) eval_hprod,
    ipc_(*)(ipc_, const rpc_[], ipc_, const int[], const rpc_[], int*, int[], rpc_[], bool, const void*) eval_shprod,
    ipc_(*)(ipc_, const rpc_[], rpc_[], const rpc_[], const void*) eval_prec
)

Find an approximation to the global minimizer of a given function subject to simple bounds on the variables using a partition-and-bound 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 ipc_, 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. -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. -99 The budget limit on function evaluations has been reached. This will happen if the limit control.max_evals is exceeded, and is quite normal for stochastic global-optimization methods. The user may explore increasing control.max_evals to see if that produces a lower value of the objective function, but there are unfortunately no guarantees.
n	is a scalar variable of type ipc_, that holds the number of variables
x	is a one-dimensional array of size n and type rpc_, that holds the values \(x\) of the optimization variables. The j-th component of x, j = 0, … , n-1, contains \(x_j\).
g	is a one-dimensional array of size n and type rpc_, that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 0, … , n-1, contains \(g_j\).
eval_f	is a user-supplied function that must have the following signature: ipc_ eval_f( ipc_ n, const rpc_ x[], rpc_ *f, const void *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: ipc_ eval_g( ipc_ n, const rpc_ x[], rpc_ g[], const void *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: ipc_ eval_hprod( ipc_ n, const rpc_ x[], rpc_ u[], const rpc_ v[], bool got_h, const void *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 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: ipc_ eval_shprod( ipc_ n, const rpc_ x[], ipc_ nnz_v, const ipc_ index_nz_v[], const rpc_ v[], ipc_ *nnz_u, ipc_ index_nz_u[], rpc_ u[], bool got_h, const void *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 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 NULL. If non-NULL, it must have the following signature: ipc_ eval_prec( ipc_ n, const rpc_ x[], rpc_ u[], const rpc_ v[], const void *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.

void dgo_solve_reverse_with_mat(
    void **data,
    ipc_ *status,
    ipc_ *eval_status,
    ipc_ n,
    rpc_ x[],
    rpc_ f,
    rpc_ g[],
    ipc_ ne,
    rpc_ H_val[],
    const rpc_ u[],
    rpc_ v[]
)

Find an approximation to the global minimizer of a given function subject to simple bounds on the variables using a partition-and-bound 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 ipc_, 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. -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. -99 The budget limit on function evaluations has been reached. This will happen if the limit control.max_evals is exceeded, and is quite normal for stochastic global-optimization methods. The user may explore increasing control.max_evals to see if that produces a lower value of the objective function, but there are unfortunately no guarantees. 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 g radient should be set in g[i], for i = 0, …, n-1 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 ipc_, that is used to indicate if objective function/gradient/Hessian values can be provided (see above)
n	is a scalar variable of type ipc_, that holds the number of variables
x	is a one-dimensional array of size n and type rpc_, that holds the values \(x\) of the optimization variables. The j-th component of x, j = 0, … , n-1, contains \(x_j\).
f	is a scalar variable pointer of type rpc_, that holds the value of the objective function.
g	is a one-dimensional array of size n and type rpc_, that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 0, … , n-1, contains \(g_j\).
ne	is a scalar variable of type ipc_, 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 rpc_, 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 rpc_, that is used for reverse communication (see above for details)
v	is a one-dimensional array of size n and type rpc_, that is used for reverse communication (see above for details)

void dgo_solve_reverse_without_mat(
    void **data,
    ipc_ *status,
    ipc_ *eval_status,
    ipc_ n,
    rpc_ x[],
    rpc_ f,
    rpc_ g[],
    rpc_ u[],
    rpc_ v[],
    ipc_ index_nz_v[],
    ipc_ *nnz_v,
    const ipc_ index_nz_u[],
    ipc_ nnz_u
)

Find an approximation to the global minimizer of a given function subject to simple bounds on the variables using a partition-and-bound 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 ipc_, 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. -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. -99 The budget limit on function evaluations has been reached. This will happen if the limit control.max_evals is exceeded, and is quite normal for stochastic global-optimization methods. The user may explore increasing control.max_evals to see if that produces a lower value of the objective function, but there are unfortunately no guarantees. 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 g radient should be set in g[i], for i = 0, …, n-1 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 ipc_, that is used to indicate if objective function/gradient/Hessian values can be provided (see above)
n	is a scalar variable of type ipc_, that holds the number of variables
x	is a one-dimensional array of size n and type rpc_, that holds the values \(x\) of the optimization variables. The j-th component of x, j = 0, … , n-1, contains \(x_j\).
f	is a scalar variable pointer of type rpc_, that holds the value of the objective function.
g	is a one-dimensional array of size n and type rpc_, that holds the gradient \(g = \nabla_xf(x)\) of the objective function. The j-th component of g, j = 0, … , n-1, contains \(g_j\).
u	is a one-dimensional array of size n and type rpc_, 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 rpc_, 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 ipc_, that is used for reverse communication (see status=7 above for details)
nnz_v	is a scalar variable of type ipc_, that is used for reverse communication (see status=7 above for details)
index_nz_u	s a one-dimensional array of size n and type ipc_, that is used for reverse communication (see status=7 above for details)
nnz_u	is a scalar variable of type ipc_, 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

void dgo_information(void **data, struct dgo_inform_type* inform, ipc_ *status)

Provides output information

Parameters:

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

void dgo_terminate(
    void **data,
    struct dgo_control_type* control,
    struct dgo_inform_type* inform
)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a struct containing control information (see dgo_control_type)
inform	is a struct containing output information (see dgo_inform_type)