Consider the function f(x, y) = (x + 20)^2 + 2(y - 10)^2. Determine the gradient
ID: 3028298 • Letter: C
Question
Consider the function f(x, y) = (x + 20)^2 + 2(y - 10)^2. Determine the gradient (with respect to x and y) of f. Starting at (0, 0), run the gradient descent algorithm BY HAND for three iterations, with a step size of 1. What is the "best guess" for the minimum of f at this point, and what are the corresponding x and y coordinates? As always, show your work as you would in a math class. Determine (analytically, as in the full and proper way using calculus - even if the answer looks obvious to you) the actual minimum value of f, along with the corresponding x and y coordinates. How far off was the algorithm (compute the Euclidean distance)? If you ran it for more iterations, would it be able to do better? Why or why not?Explanation / Answer
From algorithm of computing Euclidean distance stops as we are measuring its distance from origin itslf and as (x,y) is in plane so it contains finite orderded no.s
Now if you ran for more iterations it will never do better because here answer is fixed real no and there is no question of approximations so more iterations has no differant effect as we are certainly drawing striaght line and then we are finding its length