Optimization problem with many inequality constraints

Question

I have a maximization problem with 4 variables and six inequality constraints. This problem is already solved and I have access to its solution. However, I would like to solve it analytically (not numerically) without looking at the solution.

I am aware of Kuhn-Tucker Conditions, and I am trying to use them. But with so many constraints, it is becomes a challenge. Thus, I am writing to ask you about whether there are some tricks or some strategies to apply in this sort of optimization problems with so many constraints. For instance, is there some method to quick identify the nonbinding constraints?

Thanks for your insight!

Answer 1

There is a way to get rid of redundant constraints, constraints that can never be active. After that no, consider the case of a hexagon defined by $Ax\leq b$, all of the constraints must be kept.