Suppose that we have an objective function X ⊆ R^n → R and Y ⊂ X.
Which of the following are correct:
- Every global minimizer of f in X is global minimizer in Y
- Every local minimizer of f in Y is local minimizer in X
My answer is that 1) and 2) are correct. I want to check if my answers are correct or we can prove something other with some example.