LP only used to check whether a strictly larger than 0 solutions exists

[chivalry]

I have a decision polytope Ax<=b; with objective function max sum(x);

Actually, I don't care about the objective value. All I care is that whether the optimal can be larger than 0. What is the most efficient implementation? Thank you:D 

[Renan Garcia]

Gurobi doesn't support strict inequalities, so you could solve something like:

   Minimize

      0'x

   Subject to

      Ax <= b

      sum(x) >= epsilon

If a feasible solution exists for this optimization problem for some espilon > 0, then the answer to "whether the optimal can be larger than 0" is yes. If the decision variables are all integral, you should set epsilon := 1. Otherwise, you'll need to choose some tolerance for "larger than 0" (e.g., 1e-3) which is larger than the FeasibilityTol parameter setting (see http://www.gurobi.com/documentation/6.0/refman/feasibilitytol.html).

On May 21, 2015, at 2:34 PM, chivalry <key0...@gmail.com> wrote:

I have a decision polytope Ax<=b; with objective function max sum(x);

Actually, I don't care about the objective value. All I care is that whether the optimal can be larger than 0. What is the most efficient implementation? Thank you:D 

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