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Slack variable
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<p>In an <a href="/facts/Optimization_problem/QzwJfFEE">optimization problem</a>, a slack variable is a variable that is added to an <a href="/facts/Inequality_constraint/QLFIFlFX">inequality constraint</a> to transform it into an equality constraint. A non-negativity constraint on the slack variable is also added.: 131 </p><p>Slack variables are used in particular in <a href="/facts/Linear_programming/GduXFQxT">linear programming</a>. As with the other variables in the augmented constraints, the slack variable cannot take on negative values, as the <a href="/facts/Simplex_algorithm/9fndF6cq">simplex algorithm</a> requires them to be positive or zero. </p> <ul><li>If a slack variable associated with a constraint is <i>zero</i> at a particular <a href="/facts/Candidate_solution/cJUKNCmM">candidate solution</a>, the <a href="/facts/Constraint_(mathematics)/QLFIFlFX">constraint</a> is <a href="/facts/Binding_constraint/QLFIFlFX">binding</a> there, as the constraint restricts the possible changes from that point.</li> <li>If a slack variable is <i>positive</i> at a particular candidate solution, the constraint is <a href="/facts/Non-binding_constraint/QLFIFlFX">non-binding</a> there, as the constraint does not restrict the possible changes from that point.</li> <li>If a slack variable is <i>negative</i> at some point, the point is <a href="/facts/Feasible_region/cJUKNCmM">infeasible</a> (not allowed), as it does not satisfy the constraint.</li></ul> <p>Slack variables are also used in the <a href="/facts/Big_M_method/0xUacjkA">Big M method</a>. </p>