PROC OPTQP: ODS Tables :: SAS/OR(R) 9.22 User's Guide: Mathematical Programming

The OPTQP Procedure

ODS Tables

PROC OPTQP creates two ODS (Output Delivery System) tables by default unless you specify a value other than 1 for the PRINTLEVEL= option. The first table, "ProblemSummary," is a summary of the input QP problem. The second table, "SolutionSummary," is a brief summary of the solution status. PROC OPTQP assigns a name to each table it creates. You can use these names to reference the table when using the ODS to select tables and create output data sets. These names are listed in Table 19.2. For more information about ODS, see the SAS Output Delivery System: Procedures Guide.

If you specify a value of 2 for the PRINTLEVEL= option, then a third table, "ProblemStatistics," is produced. This table contains information about the problem data. See the section Problem Statistics for more information.

Table 19.2 ODS Tables Produced by PROC OPTQP
ODS Table Name	Description	PRINTLEVEL=
ProblemSummary	Summary of the input QP problem	1 (default)
SolutionSummary	Summary of the solution status	1 (default)
ProblemStatistics	Description of input problem data	2

A typical output of PROC OPTQP is shown in Output 19.5.

Figure 19.5 Typical OPTQP Output

The OPTQP Procedure

Problem Summary
Problem Name	BANDM
Objective Sense	Minimization
Objective Function	....1
RHS	ZZZZ0001

Number of Variables	472
Bounded Above	0
Bounded Below	472
Bounded Above and Below	0
Free	0
Fixed	0

Number of Constraints	305
LE (<=)	0
EQ (=)	305
GE (>=)	0
Range	0

Constraint Coefficients	2494

Hessian Diagonal Elements	25
Hessian Elements Above the Diagonal	16

Solution Summary
Objective Function	....1
Solution Status	Optimal
Objective Value	16352.342414

Primal Infeasibility	1.693635E-11
Dual Infeasibility	0
Bound Infeasibility	0
Duality Gap	1.5407616E-7
Complementarity	0.004075344

Iterations	26
Presolve Time	0.00
Solution Time	0.08

You can create output data sets from these tables by using the ODS OUTPUT statement. This can be useful, for example, when you want to create a report to summarize multiple PROC OPTQP runs. The output data sets corresponding to the preceding output are shown in Output 19.6, where you can also find (in the row following the heading of each data set in the display) the variable names that are used in the table definition (template) of each table.

Figure 19.6 ODS Output Data Sets

Problem Summary

Obs	Label1	cValue1	nValue1
1	Problem Name	BANDM	.
2	Objective Sense	Minimization	.
3	Objective Function	....1	.
4	RHS	ZZZZ0001	.
5			.
6	Number of Variables	472	472.000000
7	Bounded Above	0	0
8	Bounded Below	472	472.000000
9	Bounded Above and Below	0	0
10	Free	0	0
11	Fixed	0	0
12			.
13	Number of Constraints	305	305.000000
14	LE (<=)	0	0
15	EQ (=)	305	305.000000
16	GE (>=)	0	0
17	Range	0	0
18			.
19	Constraint Coefficients	2494	2494.000000
20			.
21	Hessian Diagonal Elements	25	25.000000
22	Hessian Elements Above the Diagonal	16	16.000000

Solution Summary

Obs	Label1	cValue1	nValue1
1	Objective Function	....1	.
2	Solution Status	Optimal	.
3	Objective Value	16352.342414	16352
4			.
5	Primal Infeasibility	1.693635E-11	1.693635E-11
6	Dual Infeasibility	0	0
7	Bound Infeasibility	0	0
8	Duality Gap	1.5407616E-7	0.000000154
9	Complementarity	0.004075344	0.004075
10			.
11	Iterations	26	26.000000
12	Presolve Time	0.00	0
13	Solution Time	0.08	0.078000

Problem Statistics

Optimizers can encounter difficulty when solving poorly formulated models. Information about data magnitude provides a simple gauge to determine how well a model is formulated. For example, a model whose constraint matrix contains one very large entry (on the order of $\text{[math]}$ ) can cause difficulty when the remaining entries are single-digit numbers. The PRINTLEVEL=2 option in the OPTQP procedure causes the ODS table "ProblemStatistics" to be generated. This table provides basic data magnitude information that enables you to improve the formulation of your models.

The example output in Output 19.7 demonstrates the contents of the ODS table "ProblemStatistics."

Figure 19.7 ODS Table ProblemStatistics

The OPTQP Procedure

Problem Statistics
Number of Constraint Matrix Nonzeros	4
Maximum Constraint Matrix Coefficient	2
Minimum Constraint Matrix Coefficient	1
Average Constraint Matrix Coefficient	1.25

Number of Linear Objective Nonzeros	2
Maximum Linear Objective Coefficient	3
Minimum Linear Objective Coefficient	2
Average Linear Objective Coefficient	2.5

Number of Lower Triangular Hessian Nonzeros	1
Number of Diagonal Hessian Nonzeros	2
Maximum Hessian Coefficient	20
Minimum Hessian Coefficient	2
Average Hessian Coefficient	6.75

Number of RHS Nonzeros	2
Maximum RHS	100
Minimum RHS	1
Average RHS	50.5

Maximum Number of Nonzeros per Column	2
Minimum Number of Nonzeros per Column	2
Average Number of Nonzeros per Column	2

Maximum Number of Nonzeros per Row	2
Minimum Number of Nonzeros per Row	2
Average Number of Nonzeros per Row	2

The variable names in the ODS table "ProblemStatistics" are Label $\text{[math]}$ , cValue $\text{[math]}$ , and nValue $\text{[math]}$ , similar to those shown in Figure 19.6 (but not shown in Figure 19.7).

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