feasiblity problem in CPLEX

Question

Is there an api to solve the feasibility problem (whether a feasible point exists) for a set of convex restraints in CPLEX.

Answer 1

Yes, just don't enter an objective function. cplex will give you any solution it can find or prove that there isn't a solution.

var x;
var y;
minimize 1;

subject to con1:
  x + y <= 6;
  x + y >= 7;