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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 linear objective and constraints. They are temporary objects that typically have short lifespans.

You generally build linear expressions using overloaded operators. For example, if x is a Var object, then x + 1 is a LinExpr 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).

The full list of overloaded operators on LinExpr objects is as follows: +, +=, -, -=, *, *=, /, and ** (only for exponent 2). In Python parlance, we've defined the following LinExpr functions: __add__, __radd__, __iadd__, __sub__, __rsub__, __isub__, __neg__, __mul__, __rmul__, __imul__, __div__, and __pow__.

We've also overloaded the comparison operators (==, <=, and >=), to make it easier to build constraints from linear expressions.

You can also use add or addTerms to modify expressions. The LinExpr() constructor can also be used to build expressions. Another option is quicksum; it is a more efficient version of the Python sum function. Terms can be removed from an expression using remove.

Given all these options for building expressions, you may wonder which is fastest. For small expressions, you won't need to worry about performance differences between them. If you are building lots of very large expressions (100s of terms), you will find that the LinExpr() constructor is generally going to be fastest, followed by the addTerms method, and then the quicksum function.

To add a linear constraint to your model, you generally build one or two linear expression objects (expr1 and expr2) and then use an overloaded comparison operator to build an argument for Model.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 Model.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).


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