Difference between revisions of "Slack variable"
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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|mathematical programming]] or [[Linear programming|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. | 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|mathematical programming]] or [[Linear programming|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. | ||
Latest revision as of 18:21, 18 October 2017
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=33132
Slack variable. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Slack_variable&oldid=33132
This article was adapted from an original article by M. Hazewinkel (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article