# Slack variable

From Encyclopedia of Mathematics

2020 Mathematics Subject Classification: *Primary:* 90C05 [MSN][ZBL]

*surplus 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.

**How to Cite This Entry:**

Slack variable.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Slack_variable&oldid=42116

This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article