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Expressions and Constraints

Constructor

AffExpr is an affine expression type defined by JuMP. It has three fields: a vector of coefficients, a vector of variables, and a constant. Apart from a default constructor that takes no arguments, it also has a full constructor that can be useful if you want to manually build an affine expression:

aff = AffExpr([3.0, 4.0], [x, z], 2.0)  # 3x + 4z + 2

Note that the coefficients must be floating point numbers. The matching constraint for AffExpr is LinearConstraint which is defined by an AffExpr and a lower and upper bound. If a solver interface does not support range constraints, this will automatically translated into two constraints at solve time. Constructing constraints manually is not an expected behavior and won't add the constraint to a model automatically. See below for the correct methods.

There is also QuadExpr for quadratic expressions type that also provides a default constructor that takes no arguments and a full constructor. There are four fields: two vectors of variables, a vector of coefficients, and the affine part of the expression. This is best explained by example:

aff = AffExpr([3.0, 4.0], [x, z], 2.0)  # 3x + 4z + 2
quad = QuadExpr([x,y],[x,z],[3.0,4.0],aff)  # 3x^2 + 4yz + 3x + 4z + 2

The corresponding constraint is QuadConstraint, which is expected to be a convex quadratic constraint.

Methods

  • @addConstraint(m::Model, con) - efficient way to add linear constraints. Uses macros and thus does not yet support quadratic constraints.
  • addConstraint(m::Model, con) - general way to add linear and quadratic constraints.

Constraint References

In order to manipulate constraints after creation, it is necessary to maintain a reference. For linear constraints both @addConstraint and addConstraint return an object of type ConstraintRef{LinearConstraint}. To facilitate the storage of these we provide the convenience macro, e.g.:

@defConstrRef constraintName[1:3]

That behaves like @defVar. You can then iterate over constraints and store references in this structure, e.g.:

@defVar(m, x[1:5] >= 0)
@defConstrRef myCons[1:5]
for i = 1:5
  myCons[i] = @addConstraint(m, x[i] >= i)
end

To obtain the dual of a constraint, call getDual on the constraint reference:

println(getDual(myCons[1]))

Dual information is unavailable for MIPs and has not yet been implemented for quadratic constraints.