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I am reading a paper on solving a problem using LP methods, it says

"The linear problem has $n$ variables and $m$ constraints. From linear programming theory, we know that there is an optimal solution at which the number of constraints having equality is no smaller than the number of variables"

  1. Does the "$m$ constraints" include equality constraints as well? I mean, if there are more than $n$ equality constraints, does that statement tell nothing meaningful?
  2. Why the # of equality must be $\ge n$? Can anyone easily explain it or suggest some materials? I am new to LP optimization or convex optimization.
Jayboy
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  • "Why the # of equality must be ≥n" I don't think so. The opposite is true, in my view. If you have more constraints (m) then variables (n), then you have a risk that the system cannot be solved or even optimized. – callculus42 May 09 '22 at 17:16
  • what if the problem is solvable and there exists a solution in the feasible set? – Jayboy May 10 '22 at 02:09
  • I do not really understand your question. I would answer: Then everything is ok. – callculus42 May 10 '22 at 04:43

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