Gurobi linear expression object. A linear expression consists of a constant term, plus a list of coefficient-variable pairs that capture the linear terms. Linear expressions are used to build constraints. They are temporary objects that typically have short lifespans.

The GRBLinExpr class is a sub-class of the abstract base class GRBExpr.

You generally build linear expressions using overloaded operators. For example, if x is a GRBVar object, then x + 1 is a GRBLinExpr object. Expressions can be built from constants (e.g., expr = 0), variables (e.g., expr = 1 * x + 2 * y), or from other expressions (e.g., expr2 = 2 * expr1 + x, or expr3 = expr1 + 2 * expr2). You can also modify existing expressions (e.g., expr += x, or expr2 -= expr1).

Another option for building expressions is to use the addTerms method, which adds an array of new terms at once. Terms can also be removed from an expression, using remove.

Note that the cost of building expressions depends heavily on the approach you use. While you can generally ignore this issue when building small expressions, you should be aware of a few efficiency issues when building large expressions:

  • You should avoid using expr = expr + x in a loop. It will lead to runtimes that are quadratic in the number of terms in the expression.
  • Using expr += x (or expr -= x) is much more efficient than expr = expr + x. Building a large expression by looping over += statements is reasonably efficient, but it isn't the most efficient approach.
  • The most efficient way to build a large expression is to make a single call to addTerms.

To add a linear constraint to your model, you generally build one or two linear expression objects (<span>$</span>expr1<span>$</span> and <span>$</span>expr2<span>$</span>) and then use an overloaded comparison operator to build an argument for GRBModel::addConstr. To give a few examples:

\mathrm{model.addConstr}(expr1 <= expr2) \...
...) \\
\mathrm{model.addConstr}(2*x + 3*y <= 4) \\

Once you add a constraint to your model, subsequent changes to the expression object you used to build the constraint will not change the constraint (you would use GRBModel::chgCoeff for that).

Individual terms in a linear expression can be queried using the getVar, getCoeff, and getConstant methods. You can query the number of terms in the expression using the size method.

Note that a linear expression may contain multiple terms that involve the same variable. These duplicate terms are merged when creating a constraint from an expression, but they may be visible when inspecting individual terms in the expression (e.g., when using getVar).