Consider the following problem $$ \max x_1^2+4x_1x_2+x_2^2 \\ s.t. x_1^2+x_2^2=1 $$
a. Using conditions KKT, find the candidates to be solution.
b. Using second order conditions, stablish the status of the candidates founded in a.
c. Does the problem has a unique solution?
My question
The KKT conditions that I have in my notes are only for minimization problems $\min f$.
The structure of the Theorem is Consider minimization problem f s.t. Ax< b. If x is a KKT point, then x is a minimum of f.
How can I use the Theorem I have to solve the problem?
You can restate your problem equivalently as the minimization of $-(x_1^2+4x_1x_2+x_2^2)$ subject to the same constraint. Any solution to this problem will be a solution to your problem and viceversa.