Let's say I have an integer linear programming problem (ILP) in a $n$-space. I'd like to extend a system of constraints and add a new constraint into the problem.QuestionHow do you test that the new constraint is not contrary to old ones before solve the ILP problem? What are common approaches to test a linear programming problem? I need the key words, then I'll search an answer on my the question. 
How to check a consistency between a new constraint and old ones before solution?
reference request;linear programming;model checking