Consider the function $f(x,y) = 5x^2 + 5y^2 -xy -11x +11y +11$. Consider applying Newton's Method for minimizing $f$. How many iterations are needed to reach the global minimum point? Why should we expect this answer?
The above is paraphrased from a past test. Does anyone know how to approach this kind of question?
If I'm recalling the relevant facts properly, this question is testing your basic knowledge about how Newton's method works. If you can state the idea behind Newton's method or explain what it calculates, then the answer to the quoted question follows almost immediately.
I believe the only two approaches here, then, are:
The idea behind Newton's method for optimizing a function is, at each iteration, to approximate the function with a quadratic, and then solve for the minimum of the quadratic. So when the function you're trying to optimize is already quadratic....