The OPTQP Procedure

ODS Tables

Problem Statistics

PROC OPTQP creates three ODS (Output Delivery System) tables by default. The first table, ProblemSummary, is a summary of the input QP problem. The second table, SolutionSummary, is a brief summary of the solution status. The third table, PerformanceInfo, is a summary of performance options. You can use ODS table names to select tables and create output data sets. For more information about ODS, see the SAS Output Delivery System: User's Guide.

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

If you specify the DETAILS option in the PERFORMANCE statement, then the Timing table is produced.

Table 12.3 lists all the ODS tables that can be produced by the OPTQP procedure, along with the statement and option specifications required to produce each table.

Table 12.3: ODS Tables Produced by PROC OPTQP

ODS Table Name	Description	Statement	Option
ProblemSummary	Summary of the input QP problem	PROC OPTQP	PRINTLEVEL=1 (default)
SolutionSummary	Summary of the solution status	PROC OPTQP	PRINTLEVEL=1 (default)
ProblemStatistics	Description of input problem data	PROC OPTQP	PRINTLEVEL=2
PerformanceInfo	List of performance options and their values	PROC OPTQP	PRINTLEVEL=1 (default)
Timing	Detailed solution timing	PERFORMANCE	DETAILS

A typical output of PROC OPTQP is shown in Figure 12.5.

Figure 12.5: Typical OPTQP Output

The OPTQP Procedure

Performance Information
Execution Mode	Single-Machine
Number of Threads	4

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
Solver	QP
Algorithm	Interior Point
Objective Function	....1
Solution Status	Optimal
Objective Value	16352.342037

Primal Infeasibility	1.127493E-12
Dual Infeasibility	1.684333E-12
Bound Infeasibility	4.520378E-16
Duality Gap	1.25305E-12
Complementarity	1.2956352E-8

Iterations	23
Presolve Time	0.00
Solution Time	0.23

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 that correspond to the preceding output are shown in Figure 12.6, 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 12.6: 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	Solver	QP	.
2	Algorithm	Interior Point	.
3	Objective Function	....1	.
4	Solution Status	Optimal	.
5	Objective Value	16352.342037	16352
6			.
7	Primal Infeasibility	1.127493E-12	1.127493E-12
8	Dual Infeasibility	1.684333E-12	1.684333E-12
9	Bound Infeasibility	4.520378E-16	4.520378E-16
10	Duality Gap	1.25305E-12	1.25305E-12
11	Complementarity	1.2956352E-8	1.2956352E-8
12			.
13	Iterations	23	23.000000
14	Presolve Time	0.00	0
15	Solution Time	0.23	0.230999

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 $10^9$ ) 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 Figure 12.7 demonstrates the contents of the ODS table ProblemStatistics.

Figure 12.7: 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