- This assignment was pretty well done by everyone. Everyone seems to understand Newton's method and steepest descent very well. - Difficulties were encountered in #12. Please see the solutions. The two most common mistakes were: - Part a: a lot of people said: " If f is convex, then f has a global minimizer" This isn't true. As a counter example, think of the function f(x) = e^x. This function is strictly convex as f"(x) = e^x >0 for all x, but it has no global minimizer. What is true is " f is convex implies that a global minimimum, IF IT EXISTS, can be found among the critical points of f. In other words, if f has critical points (recall f convex) then the global min can be found among those (of course I assume f continuous and differentiable). Another key factor in part A was to notice A positive definite implies that its inverse exists. So the unique critical point (and therefore global min by above) is x* = -A^(-1)*b - For part b, most people got the general idea, but some proofs had errors, e.g. - inverting vectors (makes no sense) - squaring vectors (probably the norm square is what they meant) - dividing expressions by vector (makes no sense) - Saying that the steplenght was A^(-1). The steplength is a scalar, a real number, not a matrix.