Slack Variable

In an optimization problem, a slack variable is a variable that is added to an inequality constraint to transform it into an equality. Introducing a slack variable replaces an inequality constraint with (1) an equality constraint plus (2) a non-negativity constraint on the slack variable.
For example, by introducing the slack variable s \geq 0, the inequality Ax \leq b can be converted to the equation Ax + s = b. Instead of the one inequality constraint, there is now (1) an equality constraint (Ax + s = b) and (2) a non-negativity constraint (s \geq 0).
In the Lagrange multiplier method, the slack variable is usually denoted by \lambda.