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Solution Quality Values


Table D.1 lists the quality values that are stored in a double variable, and accessed by the routine CPXgetdblquality.

Table D.1 - Double-valued Quality Information

Symbolic Constant  

Meaning  

CPX_MAX_PRIMAL_INFEAS  
To access the maximum primal infeasibility or, equivalently, the maximum bound violation including slacks for the unscaled problem.  
CPX_MAX_SCALED_PRIMAL_INFEAS  
To access the maximum primal infeasibility or, equivalently, the maximum bound violation including slacks for the scaled problem.  
CPX_SUM_PRIMAL_INFEAS  
To access the sum of primal infeasibilities or, equivalently, the sum of bound violations for the unscaled problem.  
CPX_SUM_SCALED_PRIMAL_INFEAS  
To access the sum of primal infeasibilities or, equivalently, the sum of bound violations for the scaled problem.  
CPX_MAX_DUAL_INFEAS  
To access the maximum of dual infeasibility or, equivalently, the maximum reduced-cost infeasibility for the unscaled problem.  
CPX_MAX_SCALED_DUAL_INFEAS  
To access the maximum of dual infeasibility or, equivalently, the maximum reduced-cost infeasibility for the scaled problem.  
CPX_SUM_DUAL_INFEAS  
To access the sum of dual infeasibilities or, equivalently, the sum of reduced-cost bound violations for the unscaled problem.  
CPX_SUM_SCALED_DUAL_INFEAS  
To access the sum of dual infeasibilities or, equivalently, the sum of reduced-cost bound violations for the scaled problem.  
CPX_MAX_INT_INFEAS  
To access the maximum of integer infeasibility for the unscaled problem.  
CPX_SUM_INT_INFEAS  
To access the sum of integer infeasibilities for the unscaled problem.  
CPX_MAX_PRIMAL_RESIDUAL  
To access the maximum of the vector |Ax-b| for the unscaled problem.  
CPX_MAX_SCALED_PRIMAL_RESIDUAL  
To access the maximum of the vector |Ax-b| for the scaled problem.  
CPX_SUM_PRIMAL_RESIDUAL  
To access the sum of the elements of vector |Ax-b| for the unscaled problem.  
CPX_SUM_SCALED_PRIMAL_RESIDUAL  
To access the sum of the elements of vector |Ax-b| for the unscaled problem.  
CPX_MAX_DUAL_RESIDUAL  
To access maximum dual residual value. For a simplex solution this is the maximum of the vector |c-B'pi|, and for a Barrier solution it is the maximum of the vector |A'pi+rc-c| for the unscaled problem.  
CPX_MAX_SCALED_DUAL_RESIDUAL  
To access maximum dual residual value for the scaled problem.  
CPX_SUM_DUAL_RESIDUAL  
To access the sum of the absolute values of the dual residual vector for the unscaled problem.  
CPX_SUM_SCALED_DUAL_RESIDUAL  
To access the sum of the absolute values of the dual residual vector for the scaled problem.  
CPX_MAX_COMP_SLACK  
To access the maximum violation of the complementary slack for the unscaled problem.  
This is available only for a Barrier solution.  
CPX_MAX_SCALED_COMP_SLACK  
To access the maximum violation of the complementary slack for the scaled problem.  
This is available only for a Barrier solution.  
CPX_SUM_COMP_SLACK  
To access the sum of the violations of the complementary slack for the unscaled problem.  
This is available only for a Barrier solution.  
CPX_SUM_SCALED_COMP_SLACK  
To access the sum of the violations of the complementary slacks for the scaled problem.  
This is available only for a Barrier solution.  
CPX_MAX_X  
To access the maximum absolute value in the primal solution vector for the unscaled problem.  
CPX_MAX_SCALED_X  
To access the maximum absolute value in the primal solution vector for the scaled problem.  
CPX_MAX_PI  
To access the maximum absolute value in the dual solution vector for the unscaled problem.  
CPX_MAX_SCALED_PI  
To access the maximum absolute value in the dual solution vector for the scaled problem.  
CPX_MAX_SLACK  
To access the maximum absolute slack value for the unscaled problem.  
CPX_MAX_SCALED_SLACK  
To access the maximum absolute slack value for the scaled problem.  
CPX_MAX_RED_COST  
To access the maximum absolute reduced cost value for the unscaled problem.  
CPX_MAX_SCALED_RED_COST  
To access the maximum absolute reduced cost value for the scaled problem.  
CPX_SUM_X  
To access the sum of the absolute values in the primal solution vector for the unscaled problem.  
CPX_SUM_SCALED_X  
To access the sum of the absolute values in the primal solution vector for the scaled problem.  
CPX_SUM_PI  
To access the sum of the absolute values in the dual solution vector for the unscaled problem.  
CPX_SUM_SCALED_PI  
To access the sum of the absolute values in the dual solution vector for the scaled problem.  
CPX_SUM_SLACK  
To access the sum of the absolute slack values for the unscaled problem.  
CPX_SUM_SCALED_SLACK  
To access the sum of the absolute slack values for the scaled problem.  
CPX_SUM_RED_COST  
To access the sum of the absolute reduced cost values for the unscaled problem.  
CPX_SUM_SCALED_RED_COST  
To access the sum of the absolute reduced cost values for the unscaled problem.  
CPX_KAPPA  
To access the condition number of the scaled basis matrix. This is available only for a simplex solution.  
CPX_OBJ_GAP  
To access the objective value gap between the primal and dual objective value solution. This is available only for a Barrier solution.  
CPX_DUAL_OBJ  
To access the objective value relative to the dual Barrier solution. This is available only for a Barrier solution.  
CPX_PRIMAL_OBJ  
To access the objective value relative to the prima l Barrier solution. This is available only for a Barrier solution.  

Table D.2 lists the quality values that are stored in an integer variable, and accessed by the routine CPXgetintquality.

Table D.2 - Integer-valued Quality Information

Symbolic Constant  

Meaning  

CPX_MAX_PRIMAL_INFEAS  
To access the lowest index of a column or row where the maximum primal infeasibility occurs for the unscaled problem. An index (*quality_p) < 0 indicates that the maximum occurs at the slack variable for row (-i-1).  
CPX_MAX_SCALED_PRIMAL_INFEAS  
To access the lowest index of a column or row where the maximum primal infeasibility occurs for the scaled problem.  
CPX_MAX_DUAL_INFEAS  
To access the lowest index where the maximum dual infeasibility occurs for the unscaled problem.  
CPX_MAX_SCALED_DUAL_INFEAS  
To access the lowest index where the maximum dual infeasibility occurs for the scaled problem.  
CPX_MAX_INT_INFEAS  
To access the lowest index where the maximum integer infeasibility occurs for the unscaled problem.  
CPX_MAX_SCALED_INT_INFEAS  
To access the lowest index where the maximum integer infeasibility occurs for the scaled problem.  
CPX_MAX_PRIMAL_RESIDUAL  
To access the lowest index where the maximum primal residual occurs for the unscaled problem.  
CPX_MAX_SCALED_PRIMAL_RESIDUAL  
To access the lowest index where the maximum primal residual occurs for the scaled problem.  
CPX_MAX_DUAL_RESIDUAL  
To access the lowest index where the maximum dual residual occurs for the unscaled problem.  
CPX_MAX_SCALED_DUAL_RESIDUAL  
To access the lowest index where the maximum dual residual occurs for the scaled problem.  
CPX_MAX_COMPLSLACK  
To access the lowest index of a row or column with the largest violation of the complementary slackness conditions. An index (*quality_p) < 0 denotes (the slack variable for) row (-i-1).  
This is available only for a Barrier solution.  
CPX_MAX_X  
To access the lowest index where the maximum x value occurs for the unscaled problem.  
CPX_MAX_SCALED_X  
To access the lowest index where the maximum x value occurs for the scaled problem.  
CPX_MAX_PI  
To access the lowest index where the maximum pi value occurs for the unscaled problem.  
CPX_MAX_SCALED_PI  
To access the lowest index where the maximum pi value occurs for the scaled problem.  
CPX_MAX_SLACK  
To access the lowest index where the maximum slack value occurs for the unscaled problem.  
CPX_MAX_SCALED_SLACK  
To access the lowest index where the maximum slack value occurs for the scaled problem.  
CPX_MAX_RED_COST  
To access the lowest index where the maximum reduced cost value occurs for the unscaled problem.  
CPX_MAX_SCALED_RED_COST  
To access the lowest index where the maximum reduced cost value occurs for the scaled problem.  

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