MATH 494: Mathematical Foundations of Machine Learning

Assignment #1

(Due Monday, February 12, 2024)

Consider the function f(x,y,z) = x^2+y^2+z^2-x-y+z. Write a script that uses gradient descent to find the minimum of the function. In addition to implementing gradient descent, the script should display a curve that illustrates how the change of the values of (x, y, z) between two consecutive iterations changes with respect to the iteration number. Also, determine the largest value of step size (eta - learning rate) for which the method converges.

Note 1: This is an extremely well-behaved function and the method will easily converge for small enough step size. The main purpose of the assignment is to get you accustomed to writing and executing Python scripts.

Note 2: I will be happy to answer questions about the details of the assignment in class on Monday, 2/5.