PRESOLVE

purpose

The presolve package transforms linear and quadratic programming data so that the resulting problem is easier to solve. This reduced problem may then be passed to an appropriate solver. Once the reduced problem has been solved, it is then a restored to recover the solution for the original formulation.

The package applies presolving techniques to linear programs, whose aim is to minimize the linear objective function

\[\ell(x) = f + g^T x,\]

or quadratic programs, which target the quadratic objective function

\[q(x) = f + g^T x + \frac{1}{2} x^T H x,\]

subject to the general linear constraints

\[c_i^l \leq a_i^{T}x \leq c_i^u, \;\;\; i = 1, \ldots , m,\]

and simple bounds

\[x_j^l \leq x_j^{ } \leq x_j^u , \;\;\; j = 1, \ldots , n,\]

where the scalar \(f\), the \(n\)-dimensional vectors \(g\), \(x^l\) and \(x^u\), the \(m\)-dimensional vectors \(c^l\) and \(c^u\), the \(n \times n\) symmetric matrix \(H\) and the \(m \times n\) matrix \(A\) (whose rows are the vectors \(a_i^T\)) are given. Furthermore, bounds on the Lagrange multipliers \(y\) associated with the general linear constraints and on the dual variables \(z\) associated with the simple bound constraints

\[y_i^l \leq y_i \leq y_i^u, \;\;\; i = 1, \ldots , m,\]

and

\[z_i^l \leq z_i \leq z_i^u, \;\;\; i = 1, \ldots , n,\]

are also provided, where the \(m\)-dimensional vectors \(y^l\) and \(y^u\), as well as the \(n\)-dimensional vectors \(x^l\) and \(x^u\) are given. Any component of \(c^l\), \(c^u\), \(x^l\), \(x^u\), \(y^l\), \(y^u\), \(z^l\) or \(z^u\) may be infinite.

Currently only the options and inform dictionaries are exposed; these are provided and used by other GALAHAD packages with Python interfaces. Please contact us if you would like full functionality!

See Section 4 of $GALAHAD/doc/presolve.pdf for additional details.

method

The required solution \(x\) of the problem necessarily satisfies the primal optimality conditions

\[A x = c\]

and

\[c^l \leq c \leq c^u, \;\; x^l \leq x \leq x^u,\]

the dual optimality conditions

\[H x + g = A^{T} y + z, \;\; y = y^l + y^u \;\; \mbox{and} \;\; z = z^l + z^u,\]

and

\[y^l \geq 0 , \;\; y^u \leq 0 , \;\; z^l \geq 0 \;\; \mbox{and} \;\; z^u \leq 0,\]

and the complementary slackness conditions

\[ ( A x - c^l )^{T} y^l = 0, \;\; ( A x - c^u )^{T} y^u = 0, \;\; (x -x^l )^{T} z^l = 0 \;\;\mbox{and}\;\; (x -x^u )^{T} z^u = 0, \]

where the vectors \(y\) and \(z\) are known as the Lagrange multipliers for the general linear constraints, and the dual variables for the bounds, respectively, and where the vector inequalities hold componentwise.

The purpose of presolving is to exploit these equations in order to reduce the problem to the standard form defined as follows:

• \(*\) The variables are ordered so that their bounds appear in the order

  variable bound order

  free			\(x\)
  non-negativity	0	\(\leq\)	\(x\)
  lower	\(x^l\)	\(\leq\)	\(x\)
  range	\(x^l\)	\(\leq\)	\(x\)	\(\leq\)	\(x^u\)
  upper			\(x\)	\(\leq\)	\(x^u\)
  non-positivity			\(x\)	\(\leq\)	0

  Fixed variables are removed. Within each category, the variables are further ordered so that those with non-zero diagonal Hessian entries occur before the remainder.

• \(*\) The constraints are ordered so that their bounds appear in the order

  constraint bound order

  non-negativity	0	\(\leq\)	\(A x\)
  equality	\(c^l\)	\(=\)	\(A x\)
  lower	\(c^l\)	\(\leq\)	\(A x\)
  range	\(c^l\)	\(\leq\)	\(A x\)	\(\leq\)	\(c^u\)
  upper			\(A x\)	\(\leq\)	\(c^u\)
  non-positivity			\(A x\)	\(\leq\)	0

  Free constraints are removed.

• \(*\) In addition, constraints may be removed or bounds tightened, to reduce the size of the feasible region or simplify the problem if this is possible, and bounds may be tightened on the dual variables and the multipliers associated with the problem.

The presolving algorithm proceeds by applying a (potentially long) series of simple transformations to the problem, each transformation introducing a further simplification of the problem. These involve the removal of empty and singleton rows, the removal of redundant and forcing primal constraints, the tightening of primal and dual bounds, the exploitation of linear singleton, linear doubleton and linearly unconstrained columns, the merging dependent variables, row sparsification and split equalities. Transformations are applied in successive passes, each pass involving the following actions:

• \(*\) remove empty and singletons rows,

• \(*\) try to eliminate variables that are linearly unconstrained,

• \(*\) attempt to exploit the presence of linear singleton columns,

• \(*\) attempt to exploit the presence of linear doubleton columns,

• \(*\) complete the analysis of the dual constraints,

• \(*\) remove empty and singletons rows,

• \(*\) possibly remove dependent variables,

• \(*\) analyze the primal constraints,

• \(*\) try to make \(A\) sparser by combining its rows,

• \(*\) check the current status of the variables, dual variables and multipliers.

All these transformations are applied to the structure of the original problem, which is only permuted to standard form after all transformations are completed. Note that the Hessian and Jacobian of the resulting reduced problem are always stored in sparse row-wise format. The reduced problem is then solved by a quadratic or linear programming solver, thus ensuring sufficiently small primal-dual feasibility and complementarity. Finally, the solution of the simplified problem is re-translated in the variables/constraints/format of the original problem formulation by a restoration phase.

If the number of problem transformations exceeds options['transf_buffer_size'], the transformation buffer size, then they are saved in a “history” file, whose name may be chosen by specifying the options['transf_file_name'] parameter. When this is the case, this file is subsequently reread by presolve_restore. It must not be altered by the user.

At the overall level, the presolving process follows one of the two sequences:

\(\boxed{\mbox{initialize}}\) \(\rightarrow\) \(\bigg[\) \(\boxed{\mbox{apply transformations}}\) \(\rightarrow\) (solve problem) \(\rightarrow\) \(\boxed{\mbox{restore}}\) \(\bigg]\) \(\rightarrow\) \(\boxed{\mbox{terminate}}\)

or

\(\boxed{\mbox{initialize}}\) \(\rightarrow\) \(\bigg[\) \(\boxed{\mbox{read specfile}}\) \(\rightarrow\) \(\boxed{\mbox{apply transformations}}\) \(\rightarrow\) (solve problem) \(\rightarrow\) \(\boxed{\mbox{restore}}\) \(\bigg]\) \(\rightarrow\) \(\boxed{\mbox{terminate}}\)

where the procedure’s control parameter may be modified by reading the specfile, and where (solve problem) indicates that the reduced problem is solved. Each of the “boxed” steps in these sequences corresponds to calling a specific function in the package. In the above diagrams, brackated subsequence of steps means that they can be repeated with problem having the same structure. The value of the new_problem_structure argument must be true on entry to presolve_apply on the first time it is used in this repeated subsequence. Such a subsequence must be terminated by a call to presolve_terminate before presolving is applied to a problem with a different structure.

Note that the values of the multipliers and dual variables (and thus of their respective bounds) depend on the functional form assumed for the Lagrangian function associated with the problem. This form is given by

\[L( x, y, z ) = q( x ) - {\tt y_{sign}} * y^T ( A x - c ) - {\tt z_{sign}} * z,\]

(considering only active constraints \(A x = c\)), where the parameters \({\tt y_{sign}}\) and \({\tt z_{sign}}\) are +1 or -1 and can be chosen by the user using options['y_sign'] and options['z_sign']. Thus, if \({\tt y_{sign} = +1}\), the multipliers associated to active constraints originally posed as inequalities are non-negative if the inequality is a lower bound and non-positive if it is an upper bound. Obvioulsy they are not constrained in sign for constraints originally posed as equalities. These sign conventions are reversed if \({\tt y_{sign} = -1}\). Similarly, if \({\tt z_{sign} = +1}\), the dual variables associated to active bounds are non-negative if the original bound is an lower bound, non-positive if it is an upper bound, or unconstrained in sign if the variables is fixed; and this convention is reversed in \({\tt z_{sign} = -1}\). The values of \({\tt z_{sign}}\) and \({\tt y_{sign}}\) may be chosen by setting the corresponding components of the ``options` to 1 or -1.

references

The algorithm is described in more detail in

N. I. M. Gould and Ph. L. Toint, ``Presolving for quadratic programming’’. Mathematical Programming 100(1) (2004) 95–132.

functions

presolve.initialize()

Set default option values and initialize private data.

Returns:

optionsdict

dictionary containing default control options:

terminationint

Determines the strategy for terminating the presolve analysis. Possible values are:

• 1

  presolving is continued as long as one of the sizes of the problem (n, m, a_ne, or h_ne) is being reduced;

• 2

  presolving is continued as long as problem transformations remain possible. NOTE: the maximum number of analysis passes (control.max_nbr_passes) and the maximum number of problem transformations (control.max_nbr_transforms) set an upper limit on the presolving effort irrespective of the choice of control.termination. The only effect of this latter parameter is to allow for early termination.

max_nbr_transformsint

The maximum number of problem transformations, cumulated over all calls to p presolve.

max_nbr_passesint

The maximum number of analysis passes for problem analysis during a single call of p presolve_transform_problem.

c_accuracyfloat

The relative accuracy at which the general linear constraints are satisfied at the exit of the solver. Note that this value is not used before the restoration of the problem.

z_accuracyfloat

The relative accuracy at which the dual feasibility constraints are satisfied at the exit of the solver. Note that this value is not used before the restoration of the problem.

infinityfloat

The value beyond which a number is deemed equal to plus infinity (minus infinity being defined as its opposite).

outint

The unit number associated with the device used for printout.

erroutint

The unit number associated with the device used for error ouput.

print_levelint

The level of printout requested by the user. Can take the values:

• <=0

  no printout is produced

• 1

  only reports the major steps in the analysis

• 2

  reports the identity of each problem transformation

• 3

  reports more details

• 4

  reports lots of information.

• >=5

  reports a completely silly amount of information.

dual_transformationsbool

True if dual transformations of the problem are allowed. Note that this implies that the reduced problem is solved accurately (for the dual feasibility condition to hold) as to be able to restore the problem to the original constraints and variables. False prevents dual transformations to be applied, thus allowing for inexact solution of the reduced problem. The setting of this control parameter overides that of get_z, get_z_bounds, get_y, get_y_bounds, dual_constraints_freq, singleton_columns_freq, doubleton_columns_freq, z_accuracy, check_dual_feasibility.

redundant_xcbool

True if the redundant variables and constraints (i.e. variables that do not appear in the objective function and appear with a consistent sign in the constraints) are to be removed with their associated constraints before other transformations are attempted.

primal_constraints_freqint

The frequency of primal constraints analysis in terms of presolving passes. A value of j = 2 indicates that primal constraints are analyzed every 2 presolving passes. A zero value indicates that they are never analyzed.

dual_constraints_freqint

The frequency of dual constraints analysis in terms of presolving passes. A value of j = 2 indicates that dual constraints are analyzed every 2 presolving passes. A zero value indicates that they are never analyzed.

singleton_columns_freqint

The frequency of singleton column analysis in terms of presolving passes. A value of j = 2 indicates that singleton columns are analyzed every 2 presolving passes. A zero value indicates that they are never analyzed.

doubleton_columns_freqint

The frequency of doubleton column analysis in terms of presolving passes. A value of j indicates that doubleton columns are analyzed every 2 presolving passes. A zero value indicates that they are never analyzed.

unc_variables_freqint

The frequency of the attempts to fix linearly unconstrained variables, expressed in terms of presolving passes. A value of j = 2 indicates that attempts are made every 2 presolving passes. A zero value indicates that no attempt is ever made.

dependent_variables_freqint

The frequency of search for dependent variables in terms of presolving passes. A value of j = 2 indicates that dependent variables are searched for every 2 presolving passes. A zero value indicates that they are never searched for.

sparsify_rows_freqint

The frequency of the attempts to make A sparser in terms of presolving passes. A value of j = 2 indicates that attempts are made every 2 presolving passes. A zero value indicates that no attempt is ever made.

max_fillint

The maximum percentage of fill in each row of A. Note that this is a row-wise measure: globally fill never exceeds the storage initially used for A, no matter how large control.max_fill is chosen. If max_fill is negative, no limit is put on row fill.

transf_file_nbrint

The unit number to be associated with the file(s) used for saving problem transformations on a disk file.

transf_buffer_sizeint

The number of transformations that can be kept in memory at once (that is without being saved on a disk file).

transf_file_statusint

The exit status of the file where problem transformations are saved:

• 0

  the file is not deleted after program termination

• 1

  the file is not deleted after program termination.

transf_file_namestr

The name of the file (to be) used for storing problem transformation on disk. NOTE: this parameter must be identical for all calls to p presolve following p presolve_read_specfile. It can then only be changed after calling presolve_terminate.

y_signint

Determines the convention of sign used for the multipliers associated with the general linear constraints.

• 1

  All multipliers corresponding to active inequality constraints are non-negative for lower bound constraints and non-positive for upper bounds constraints.

• -1

  All multipliers corresponding to active inequality constraints are non-positive for lower bound constraints and non-negative for upper bounds constraints.

inactive_yint

Determines whether or not the multipliers corresponding to constraints that are inactive at the unreduced point corresponding to the reduced point on input to p presolve_restore_solution must be set to zero. Possible values are: associated with the general linear constraints.

• 0

  All multipliers corresponding to inactive inequality constraints are forced to zero, possibly at the expense of deteriorating the dual feasibility condition.

• 1

  Multipliers corresponding to inactive inequality constraints are left unaltered.

z_signint

Determines the convention of sign used for the dual variables associated with the bound constraints.

• 1

  All dual variables corresponding to active lower bounds are non-negative, and non-positive for active upper bounds.

• -1

  All dual variables corresponding to active lower bounds are non-positive, and non-negative for active upper bounds.

inactive_zint

Determines whether or not the dual variables corresponding to bounds that are inactive at the unreduced point corresponding to the reduced point on input to presolve_restore_solution must be set to zero. Possible values are: associated with the general linear constraints.

• 0

  All dual variables corresponding to inactive bounds are forced to zero, possibly at the expense of deteriorating the dual feasibility condition.

• 1

  Dual variables corresponding to inactive bounds are left unaltered.

final_x_boundsint

The type of final bounds on the variables returned by the package. This parameter can take the values:

• 0

  the final bounds are the tightest bounds known on the variables (at the risk of being redundant with other constraints, which may cause degeneracy);

• 1

  the best known bounds that are known to be non-degenerate. This option implies that an additional real workspace of size 2 * n must be allocated.

• 2

  the loosest bounds that are known to keep the problem equivalent to the original problem. This option also implies that an additional real workspace of size 2 * n must be allocated. NOTE: this parameter must be identical for all calls to presolve (except presolve_initialize).

final_z_boundsint

The type of final bounds on the dual variables returned by the package. This parameter can take the values:

• 0

  the final bounds are the tightest bounds known on the dual variables (at the risk of being redundant with other constraints, which may cause degeneracy);

• 1

  the best known bounds that are known to be non-degenerate. This option implies that an additional real workspace of size 2 * n must be allocated.

• 2

  the loosest bounds that are known to keep the problem equivalent to the original problem. This option also implies that an additional real workspace of size 2 * n

must be allocated. NOTE: this parameter must be identical for all calls to presolve (except presolve_initialize).

final_c_boundsint

The type of final bounds on the constraints returned by the package. This parameter can take the values:

• 0

  the final bounds are the tightest bounds known on the constraints (at the risk of being redundant with other constraints, which may cause degeneracy);

• 1

  the best known bounds that are known to be non-degenerate. This option implies that an additional real workspace of size 2 * m must be allocated.

• 2

  the loosest bounds that are known to keep the problem equivalent to the original problem. This option also implies that an additional real workspace of size 2 * n must be allocated. NOTES: 1) This parameter must be identical for all calls to presolve (except presolve_initialize). 2) If different from 0, its value must be identical to that of control.final_x_bounds.

final_y_boundsint

The type of final bounds on the multipliers returned by the package. This parameter can take the values:

• 0 the final bounds are the tightest bounds known on the multipliers (at the risk of being redundant with other constraints, which may cause degeneracy);

• 1 the best known bounds that are known to be non-degenerate. This option implies that an additional real workspace of size 2 * m must be allocated.

• 2

  the loosest bounds that are known to keep the problem equivalent to the original problem. This option also implies that an additional real workspace of size 2 * n must be allocated. NOTE: this parameter must be identical for all calls to presolve (except presolve_initialize).

check_primal_feasibilityint

The level of feasibility check (on the values of x) at the start of the restoration phase. This parameter can take the values:

• 0

  no check at all;

• 1

  the primal constraints are recomputed at x and a message issued if the computed value does not match the input value, or if it is out of bounds (if control.print_level >= 2);

• 2

  the same as for 1, but presolve is terminated if an incompatibilty is detected.

check_dual_feasibilityint

The level of dual feasibility check (on the values of x, y and z) at the start of the restoration phase. This parameter can take the values:

• 0

  no check at all;

• 1

  the dual feasibility condition is recomputed at ( x, y, z ) and a message issued if the computed value does not match the input value (if control.print_level >= 2);

• 2

  the same as for 1, but presolve is terminated if an incompatibilty is detected. The last two values imply the allocation of an additional real workspace vector of size equal to the number of variables in the reduced problem.

pivot_tolfloat

The relative pivot tolerance above which pivoting is considered as numerically stable in transforming the coefficient matrix A. A zero value corresponds to a totally unsafeguarded pivoting strategy (potentially unstable).

min_rel_improvefloat

The minimum relative improvement in the bounds on x, y and z for a tighter bound on these quantities to be accepted in the course of the analysis. More formally, if lower is the current value of the lower bound on one of the x, y or z, and if new_lower is a tentative tighter lower bound on the same quantity, it is only accepted if new_lower >= lower + tol * MAX( 1, ABS( lower ) ), where tol = control.min_rel_improve. Similarly, a tentative tighter upper bound new_upper only replaces the current upper bound upper if new_upper <= upper - tol * MAX( 1, ABS( upper ) ). Note that this parameter must exceed the machine precision significantly.

max_growth_factorfloat

The maximum growth factor (in absolute value) that is accepted between the maximum data item in the original problem and any data item in the reduced problem. If a transformation results in this bound being exceeded, the transformation is skipped.

[optional] presolve.information()

Provide optional output information.

Returns:

informdict

dictionary containing output information:

statusint

The presolve exit condition. It can take the following values (symbol in parentheses is the related Fortran code):

• 0 (OK)

  successful exit;

• 1 (MAX_NBR_TRANSF)

  the maximum number of problem transformation has been reached NOTE: this exit is not really an error, since the problem can nevertheless be permuted and solved. It merely signals that further problem reduction could possibly be obtained with a larger value of the parameter control.max_nbr_transforms

• -1 (MEMORY_FULL)

  memory allocation failed

• -2 (FILE_NOT_OPENED)

  a file intended for saving problem transformations could not be opened;

• -3 (COULD_NOT_WRITE)

  an IO error occurred while saving transformations on the relevant disk file;

• -4 (TOO_FEW_BITS_PER_BYTE)

  an integer contains less than NBRH + 1 bits.

• -21 (PRIMAL_INFEASIBLE)

  the problem is primal infeasible;

• -22 (DUAL_INFEASIBLE)

  the problem is dual infeasible;

• -23 (WRONG_G_DIMENSION)

  the dimension of the gradient is incompatible with the problem dimension;

• -24 (WRONG_HVAL_DIMENSION)

  the dimension of the vector containing the entries of the Hessian is erroneously specified;

• -25 (WRONG_HPTR_DIMENSION)

  the dimension of the vector containing the addresses of the first entry of each Hessian row is erroneously specified;

• -26 (WRONG_HCOL_DIMENSION)

  the dimension of the vector containing the column indices of the nonzero Hessian entries is erroneously specified;

• -27 (WRONG_HROW_DIMENSION)

  the dimension of the vector containing the row indices of the nonzero Hessian entries is erroneously specified;

• -28 (WRONG_AVAL_DIMENSION)

  the dimension of the vector containing the entries of the Jacobian is erroneously specified;

• -29 (WRONG_APTR_DIMENSION)

  the dimension of the vector containing the addresses of the first entry of each Jacobian row is erroneously specified;

• -30 (WRONG_ACOL_DIMENSION)

  the dimension of the vector containing the column indices of the nonzero Jacobian entries is erroneously specified;

• -31 (WRONG_AROW_DIMENSION)

  the dimension of the vector containing the row indices of the nonzero Jacobian entries is erroneously specified;

• -32 (WRONG_X_DIMENSION)

  the dimension of the vector of variables is incompatible with the problem dimension;

• -33 (WRONG_XL_DIMENSION)

  the dimension of the vector of lower bounds on the variables is incompatible with the problem dimension;

• -34 (WRONG_XU_DIMENSION)

  the dimension of the vector of upper bounds on the variables is incompatible with the problem dimension;

• -35 (WRONG_Z_DIMENSION)

  the dimension of the vector of dual variables is incompatible with the problem dimension;

• -36 (WRONG_ZL_DIMENSION)

  the dimension of the vector of lower bounds on the dual variables is incompatible with the problem dimension;

• -37 (WRONG_ZU_DIMENSION)

  the dimension of the vector of upper bounds on the dual variables is incompatible with the problem dimension;.

• -38 (WRONG_C_DIMENSION)

  the dimension of the vector of constraints values is incompatible with the problem dimension;

• -39 (WRONG_CL_DIMENSION)

  the dimension of the vector of lower bounds on the constraints is incompatible with the problem dimension;

• -40 (WRONG_CU_DIMENSION)

  the dimension of the vector of upper bounds on the constraints is incompatible with the problem dimension;

• -41 (WRONG_Y_DIMENSION)

  the dimension of the vector of multipliers values is incompatible with the problem dimension;

• -42 (WRONG_YL_DIMENSION)

  the dimension of the vector of lower bounds on the multipliers is incompatible with the problem dimension;

• -43 (WRONG_YU_DIMENSION)

  the dimension of the vector of upper bounds on the multipliers is incompatible with the problem dimension;

• -44 (STRUCTURE_NOT_SET)

  the problem structure has not been set or has been cleaned up before an attempt to analyze;

• -45 (PROBLEM_NOT_ANALYZED)

  the problem has not been analyzed before an attempt to permute it;

• -46 (PROBLEM_NOT_PERMUTED)

  the problem has not been permuted or fully reduced before an attempt to restore it

• -47 (H_MISSPECIFIED)

  the column indices of a row of the sparse Hessian are not in increasing order, in that they specify an entry above the diagonal;

• -48 (CORRUPTED_SAVE_FILE)

  one of the files containing saved problem transformations has been corrupted between writing and reading;

• -49 (WRONG_XS_DIMENSION)

  the dimension of the vector of variables’ status is incompatible with the problem dimension;

• -50 (WRONG_CS_DIMENSION)

  the dimension of the vector of constraints’ status is incompatible with the problem dimension;

• -52 (WRONG_N)

  the problem does not contain any (active) variable;

• -53 (WRONG_M)

  the problem contains a negative number of constraints;

• -54 (SORT_TOO_LONG)

  the vectors are too long for the sorting routine;

• -55 (X_OUT_OF_BOUNDS)

  the value of a variable that is obtained by substitution from a constraint is incoherent with the variable’s bounds. This may be due to a relatively loose accuracy on the linear constraints. Try to increase control.c_accuracy.

• -56 (X_NOT_FEASIBLE)

  the value of a constraint that is obtained by recomputing its value on input of p presolve_restore_solution from the current x is incompatible with its declared value or its bounds. This may caused the restored problem to be infeasible.

• -57 (Z_NOT_FEASIBLE)

  the value of a dual variable that is obtained by recomputing its value on input to \p presolve_restore_solution (assuming dual feasibility) from the current values of \((x, y, z)\) is incompatible with its declared value. This may caused the restored problem to be infeasible or suboptimal.

• -58 (Z_CANNOT_BE_ZEROED)

  a dual variable whose value is nonzero because the corresponding primal is at an artificial bound cannot be zeroed while maintaining dual feasibility (on restoration). This can happen when \(( x, y, z)\) on input of RESTORE are not (sufficiently) optimal.

• -60 (UNRECOGNIZED_KEYWORD)

  a keyword was not recognized in the analysis of the specification file

• -61 (UNRECOGNIZED_VALUE)

  a value was not recognized in the analysis of the specification file

• -63 (G_NOT_ALLOCATED)

  the vector G has not been allocated although it has general values

• -64 (C_NOT_ALLOCATED)

  the vector C has not been allocated although m > 0

• -65 (AVAL_NOT_ALLOCATED)

  the vector A.val has not been allocated although m > 0

• -66 (APTR_NOT_ALLOCATED)

  the vector A.ptr has not been allocated although m > 0 and A is stored in row-wise sparse format

• -67 (ACOL_NOT_ALLOCATED)

  the vector A.col has not been allocated although m > 0 and A is stored in row-wise sparse format or sparse coordinate format

• -68 (AROW_NOT_ALLOCATED)

  the vector A.row has not been allocated although m > 0 and A is stored in sparse coordinate format

• -69 (HVAL_NOT_ALLOCATED)

  the vector H.val has not been allocated although H.ne > 0

• -70 (HPTR_NOT_ALLOCATED)

  the vector H.ptr has not been allocated although H.ne > 0 and H is stored in row-wise sparse format

• -71 (HCOL_NOT_ALLOCATED)

  the vector H.col has not been allocated although H.ne > 0 and H is stored in row-wise sparse format or sparse coordinate format

• -72 (HROW_NOT_ALLOCATED)

  the vector H.row has not been allocated although H.ne > 0 and A is stored in sparse coordinate format

• -73 (WRONG_ANE)

  incompatible value of A_ne

• -74 (WRONG_HNE)

  incompatible value of H_ne.

nbr_transformsint

The final number of problem transformations, as reported to the user at exit.

messagestr

A few lines containing a description of the exit condition on exit of PRESOLVE, typically including more information than indicated in the description of control.status above. It is printed out on device errout at the end of execution if control.print_level >= 1.

presolve.finalize()

Deallocate all internal private storage.