callable functions

    function expo_initialize(T, INT, data, control, inform)

Set default control values and initialize private data

Parameters:

data	holds private internal data
control	is a structure containing control information (see expo_control_type)
inform	is a structure containing output information (see expo_inform_type)

    function expo_read_specfile(T, INT, 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/expo/EXPO.template. See also Table 2.1 in the Fortran documentation provided in $GALAHAD/doc/expo.pdf for a list of how these keywords relate to the components of the control structure.

Parameters:

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

    function expo_import(T, INT, control, data, status, n, m,
                        J_type, J_ne, J_row, J_col, J_ptr,
                        H_type, H_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 expo_control_type)
data	holds private internal data
status	is a scalar variable of type INT 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 restrictions n > 0, m > 0 or requirement that J/H_type contains its relevant string ‘dense’, ‘dense_by_columns’, ‘coordinate’, ‘sparse_by_rows’, ‘sparse_by_columns’, ‘diagonal’ or ‘absent’ has been violated.
n	is a scalar variable of type INT that holds the number of variables.
m	is a scalar variable of type INT that holds the number of general constraints.
J_type	is a one-dimensional array of type Vararg{Cchar} that specifies the unsymmetric storage scheme used for the Jacobian, \(J\). It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’ or ‘absent’, the latter if access to the Jacobian is via matrix-vector products; lower or upper case variants are allowed.
J_ne	is a scalar variable of type INT that holds the number of entries in \(J\) in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes.
J_row	is a one-dimensional array of size J_ne and type INT that holds the row indices of \(J\) in the sparse co-ordinate storage scheme. It need not be set for any of the other schemes, and in this case can be C_NULL.
J_col	is a one-dimensional array of size J_ne and type INT that holds the column indices of \(J\) 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.
J_ptr	is a one-dimensional array of size m+1 and type INT that holds the starting position of each row of \(J\), 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.
H_type	is a one-dimensional array of type Vararg{Cchar} that specifies the symmetric storage scheme used for the Hessian, \(H_L\). It should be one of ‘coordinate’, ‘sparse_by_rows’, ‘dense’, ‘diagonal’ or ‘absent’, the latter if access to \(H\) is via matrix-vector products; lower or upper case variants are allowed.
H_ne	is a scalar variable of type INT that holds the number of entries in the lower triangular part of \(H_L\) 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 H_ne and type INT that holds the row indices of the lower triangular part of \(H_L\) 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 H_ne and type INT that holds the column indices of the lower triangular part of \(H_L\) 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 INT 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 expo_reset_control(T, INT, 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 expo_control_type)
data	holds private internal data
status	is a scalar variable of type INT 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 expo_solve_hessian_direct(T, INT, data, userdata, status,
                                       n, m, j_ne, h_ne,
                                       c_l, c_u, x_l, x_u,
                                       x, y, z, c, gl,
                                       eval_fc, eval_gj, eval_hl)

Find a local minimizer of the constrained optimization problem using the exponential penalty method.

This call is for the case where the Hessian of the Lagrangian function is available specifically, and all function/derivative information is available by (direct) 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 INT 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’, or ‘diagonal’ has been violated. -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. -17 The step is too small to make further impact. -18 Too many iterations have been performed. This may happen if control.max_it or control.max_eval 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 INT that holds the number of variables.
m	is a scalar variable of type INT that holds the number of residuals.
j_ne	is a scalar variable of type INT that holds the number of entries in \(J\).
h_ne	is a scalar variable of type INT that holds the number of entries in the lower triangular part of \(H_L\).
c_l	is a one-dimensional array of size m and type T that holds the values \(c_l\) of the lower bounds on the constraint functions \(c(x)\). The j-th component of c_l, \(i = 1, \ldots, m\), contains \(c_{li}\).
c_u	is a one-dimensional array of size m and type T that holds the values \(c_u\) of the upper bounds on the constraint functionss \(c(x)\). The j-th component of c_u, \(i = 1, \ldots, m\), contains \(c_{ui}\).
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 \(x_{lj}\).
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 \(x_{uj}\).
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 \(x_j\). This should be set on input to an estimate of the minimizer.
y	is a one-dimensional array of size m and type T that holds the values \(y\) of the Lagrange multipliers. The j-th component of y, i = 1, … , m, contains \(y_i\).
z	is a one-dimensional array of size n and type T that holds the values \(z\) of the dual variables. The j-th component of z, j = 1, … , n, contains \(z_j\).
c	is a one-dimensional array of size m and type T that holds the constraint functions \(c(x)\). The i-th component of c, i = 1, … , m, contains \(c_i(x)\).
gl	is a one-dimensional array of size n and type T that holds the gradient \(g_L(x,y,z) = \nabla_xf(x)\) of the Lagrangian function. The j-th component of gl, j = 1, … , n, contains \(g_{Lj}\).
eval_fc	is a user-supplied function that must have the following signature: function eval_c(n, x, f, c, userdata) The value of the objective function \(f(x)\) and the components of the residual function \(c(x)\) evaluated at x=\(x\) must be assigned to f and c, respectively, 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_fc via the structure userdata.
eval_gj	is a user-supplied function that must have the following signature: function eval_j(n, m, j_ne, x, g, j, userdata) The components of the gradient \(g = g(x)\) of the objective and Jacobian \(J = \nabla_x c(x\)) of the constraints evaluated at x=\(x\) must be assigned to g and to j, in the same order as presented to expo_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_gj via the structure userdata.
eval_hl	is a user-supplied function that must have the following signature: function eval_hl(n, m, h_ne, x, y, h, userdata) The nonzeros of the Hessian of the Lagrangian function \(H_L(x,y) = \nabla_{xx}f(x) -\sum_i y_i \nabla_{xx}c_i(x)\) evaluated at x=\(x\) and y=\(y\) must be assigned to h in the same order as presented to expo_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_hl via the structure userdata.

    function expo_information(T, INT, data, inform, status)

Provides output information

Parameters:

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

    function expo_terminate(T, INT, data, control, inform)

Deallocate all internal private storage

Parameters:

data	holds private internal data
control	is a structure containing control information (see expo_control_type)
inform	is a structure containing output information (see expo_inform_type)