I am currently using Gurobi to check the feasibility of a set of constraints Ax<=b by simply checking whether the solver returns infeasible or not. If it is feasible I add another constraint cx<=d and check if the constraints Ax<=b and cx<=d is feasible and so on until the model is infeasible...
Are there any parameters that are useful for doing this more efficiently than just starting from scratch each time? For example, is it possible to get the indices of the redundant constraints detected in the presolve? This would make the number of constraints that need to be considered in subsequent steps fewer. Furthermore, is it possible to pass a parameter which signifies that one is only interested in feasibility which could make Gurobi return infeasible/feasible faster?
I am using the MATLAB API which might make things more limiting.
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