According to my understanding, we should put a slack variable to equate an inequality constraint by inserting the slack variable in the side that is less than the other side. For example, if we have $4x+2<2$ this will be $4x+2+\text{slack_variable}=2$.

But in the example section of the Slack Variable Wikipedia, it says the following:

By introducing the slack variable $y\ge0$, the inequality $Ax\le b$ can be converted to the equation $y-Ax+b = 0$.

Which means that the slack variable is inserted on the bigger side! Please someone explain this confusion.

  • 6
    $\begingroup$ The Wikipedia example is wrong. It should be $Ax+y=b$. $\endgroup$
    – RobPratt
    Apr 7 '20 at 3:20
  • 2
    $\begingroup$ FYI, I just fixed the Wikipedia entry. $\endgroup$
    – prubin
    Apr 7 '20 at 22:15
  • $\begingroup$ Many thanks for all of you . $\endgroup$
    – John adams
    Apr 7 '20 at 22:52

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