The OPTMODEL Procedure

CONSTRAINT Declaration

CONSTRAINT constraint [, ...constraint];

CON constraint [, ...constraint];

The constraint declaration defines one or more constraints on expressions in terms of the optimization variables. You can specify multiple constraint declaration statements.

Constraints can have an upper bound, a lower bound, or both bounds. The allowed forms are as follows:

[ name [ { index-set } ] : ] expression = expression

declares an equality constraint or, when an index-set is specified, a family of equality constraints. The solver attempts to assign values to the optimization variables to make the two expressions equal.

[ name [ { index-set } ] : ] expression relation expression

declares an inequality constraint that has a single upper or lower bound. When an index-set is specified, this declares a family of inequality constraints. Relation is the <= or >= operator. The solver tries to assign optimization variable values so that the left expression has a value less than or equal to (respectively, greater than or equal to) the right expression value.

[ name [ { index-set } ] : ] bound relation body relation bound

declares an inequality constraint that is bounded on both sides, or range constraint. When an index-set is specified, this declares a family of range constraints. Relation is the <= or >= operator. The same operator must be used in both positions. The first bound expression defines the lower bound (respectively, upper bound). The second bound expression defines the upper bound (respectively, lower bound). The solver tries to assign optimization variables so that the value of the body expression is in the range between the upper and lower bounds.

Name defines the name for the constraint. Use the name to reference constraint attributes, such as the bounds, elsewhere in the PROC OPTMODEL model. If no name is provided, then a default name is created of the form _ACON_[], where is an integer. See the section "Constraints" for more information.

Here is a simple example that defines a constraint with a lower bound:

  
    proc optmodel; 
       var x, y; 
       number low; 
       con a: x+y >= low;
 

The following example adds an upper bound:

  
    var x, y; 
    number low; 
    con a: low <= x+y <= low+10;
 

Indexed families of constraints can be defined by specifying an index-set after the name. Any dummy parameters that are declared in the index-set can be referenced in the expressions that define the constraint. A particular member of a indexed family can be specified using an identifier-expression with a bracketed index list, in the same fashion as array parameters and variables. For example, the following code creates an indexed family of constraints named incr:

  
    proc optmodel; 
       number n; 
       var x{1..n} 
       /* require nondecreasing x values */ 
       con incr{i in 1..n-1}: x[i+1] >= x[i];
 

The CON statement in the example creates constraints incr[1] through incr[1].

Constraint expressions cannot be defined using functions that return different values each time they are called. See the section "Indexing" for details.