# Slack variable

A non-negative variable $y_i$ that is introduced for a (linear) constraint $\sum_ja_{ij}x_j\leq b_i$ in a mathematical programming or linear programming problem to convert this inequality into an equality $y_i+\sum_ja_{ij}x_j=b_i$. If this is done for all inequalities in a linear programming problem, one sometimes speaks of logical variables.