Overview over Kuhn-Tucker approach

The basics of the Kuhn-Tucker approach is to set up the Lagrange function, write down the necessary constraints (F.O.C's, constraints on multipliers and so on), find candidates that satisfy these, then compare the candidates and find the best. If possible, verify sufficient conditions. We have two tools: check concacity of the Lagrange function, or see if you have a closed and bounded set of variable choices (extreme value theorem).

Remember that if you have a minimization problem, just make it into a maximization problem by knowing that min(f)=max(-f). All else is unchanged, so do not change the constraints! Then the optimal function of the min. problem is W=-V, where V is the optimal function of the max version.

Also, you now know how to see how the optimized function changes value when a parameter of the problem is changed. First, before changing the parameter, find the optimal x. Then, find the partial derivative of Lagrange function w.r.t. parameter, and incert optimal x. By the envelope theorem, this equals the derivative of value function w.r.t. the parameter.

Also remember that we covered some special cases.