To keep the same Holant value, each the new vertices is assigned the binary equality constraint.

There are two types of constraints: equality constraints and inequality constraints.

Linear and nonlinear programming have profoundly affected microeconomics, which had earlier considered only equality constraints.

We note that this set of constraint equations encompass a very general variety of holonomic and non-holonomic equality constraints.

A slight modification of the procedure will enable us to add equality constraints.

The general procedure, given an equality constraint, is to add whichever inequality is not satisfied by the current solution.

Note that every equality constraint can be equivalently replaced by a pair of inequality constraints and .

Therefore, for theoretical purposes, equality constraints are redundant; however, it can be beneficial to treat them specially in practice.

Quadratic programming is particularly simple when there are only equality constraints; specifically, the problem is linear.

Finally, it is also possible to handle additional equality constraints: