NLINCON Statement

The NLP Procedure

NLINCON Statement

NLINCON nlcon [ , nlcon ...] [ / option ] ;

NLC nlcon [ , nlcon ...] [ / option ] ;


where nlcon := number operator variable_list operator number 
or 		 nlcon := number operator variable_list 
or 		 nlcon := variable_list operator number 
and 		 operator := <= | < | >= | > | = 
and 		 option := SUMOBS | EVERYOBS

General nonlinear equality and inequality constraints are specified with the NLINCON statement. The syntax of the NLINCON statement is similar to that of the BOUNDS statement with two small additions:

The BOUNDS statement can only contain the names of decision variables. In addition, the NLINCON statement can contain the names of continuous functions of the decision variables. These must be computed in the program statements and since they can depend on the values of some of the variables in the DATA= data set there are two possibilities:
- The continuous functions should be summarized across all observations read from the DATA= data set. In this case the NLINCON statement must be terminated by the / SUMOBS option .
- The continuous functions should be evaluated separately for every observation in the data set. In this case the NLINCON statement must be terminated by the / EVERYOBS option . For each observation of the data set one constraint is generated.
- The continuous functions should be evalutated only once for the entire data set. In this case the NLINCON statement has the same form as the BOUNDS statement. If this constraint does depend on the values of variables in the DATA= data set, it is evaluated using the data of the first observation.

One- or two-sided constraints can be specified in the NLINCON statement however, equality constraints must be one-sided. The pairs of operators (<,<=) and (>,>=) are treated in the same way.

These three statements require the values of the three functions v₁, v₂, v₃ to be between zero and ten and are equivalent:

   nlincon 0 <= v1 - v3,
           v1 - v3 <= 10;

   nlincon 0 <= v1 - v3 <= 10;

   nlincon 10 >= v1 - v3 >= 0;

Also, consider the Rosen-Suzuki Problem. It has three nonlinear inequality constraints:

$8 - x_1^2 - x_2^2 - x_3^2 - x_4^2 - x_1 + x_2 - x_3 + x_4 \geq 0$

$10 - x_1^2 - 2 x_2^2 - x_3^2 - 2 x_4^2 + x_1 + x_4 \geq 0$

$5 - 2 x_1^2 - x_2^2 - x_3^2 - 2 x_1 + x_2 + x_4 \geq 0$

These are specified as:

  nlincon c1 - c3 >= 0;

  c1 = 8 - x1 * x1 - x2 * x2 - x3 * x3 - x4 * x4 -
         x1 + x2 - x3 + x4;
  c2 = 10 - x1 * x1 - 2 * x2 * x2 - x3 * x3 - 2 * x4 * x4 +
         x1 + x4;
  c3 = 5 - 2 * x1 * x1 - x2 * x2 - x3 * x3 - 2 * x1 + x2 + x4;

Note: QUANEW and NMSIMP are the only optimization subroutines that support the NLINCON statement.

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