In an optimization problem, a **slack variable** is a variable that is added to an inequality constraint to transform it to an equality. Introducing a slack variable replaces an inequality constraint with an equality constraint and a nonnegativity constraint.

In linear programming, this is required to turn an inequality into an equality where a linear combination of variables is less than or equal to a given constant in the former. As with the other variables in the augmented constraints, the slack variable cannot take on negative values, as the Simplex algorithm requires them to be positive or zero.

- If a slack variable associated with a constraint is
*zero*in a given state, the constraint is**binding**, as the constraint restricts the possible changes of the point. - If a slack variable is
*positive*in a given state, the constraint is**non-binding**, as the constraint does not restrict the possible changes of the point. - If a slack variable is
*negative*in a given state, the point is**infeasible**, and not allowed, as it does not satisfy the constraint.

Read more about Slack Variable: Example, Embedding in Orthant, See Also

### Other articles related to "variable, slack variable":

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**variable**in the primal space corresponds an inequality to satisfy in the dual space, both indexed by output type ... satisfy in the primal space corresponds a

**variable**in the dual space, both indexed by input type ... Since each inequality can be replaced by an equality and a

**slack variable**, this means each primal

**variable**corresponds to a dual

**slack variable**, and each dual

**variable**...

### Famous quotes containing the words variable and/or slack:

“There is not so *variable* a thing in nature as a lady’s head-dress.”

—Joseph Addison (1672–1719)

“In marriage, a man becomes *slack* and selfish, and undergoes a fatty degeneration of his moral being.”

—Robert Louis Stevenson (1850–1894)