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My question is in the title:

How can we define exactly when two linear programming problems are equivalent?

I used to see some definition such as "$B$ is equivalent to $A$ if $B$ is solvable, then $A$ is solvable", but it is quite confusing to use this definition to check whether two LP problems are equivalent.

Thanks in advance.

Tien Kha Pham
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    Without even recalling the definition of L.P. Problem, I'd risk calling them equivalent if the solution set is the same. Edit: Having re-read the definition of L.P.Problem, I stand by my risk. – Git Gud Jan 14 '16 at 08:23
  • @GitGud there are many cases the solution set can't be the same, because they are in different spaces. For example, when you need to add some slack variables to a LP to make it into standard form, the solution sets are not the same at all. – Tien Kha Pham Jan 14 '16 at 08:30
  • Of course they are. Slack isn't part of the solution. – Benjamin Lindqvist Jan 15 '16 at 10:02

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