linear programming and the number of equality constraints

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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.