(Solved): Problem 3: Write a MATLAB script called hw4_p3.m to use Newton's method of optimization to find th ...

Problem 3: Write a MATLAB script called hw4_p3.m to use Newton's method of optimization to find the minimum of ƒ(x) = 40x² + x². Use x(0) = [20, 20] as the starting point and || ? f(x)|| < 10-6 as the stopping criterion. Discuss your results: Why did the algorithm work the way it did? Note: In class, we went over Newton's method of optimization for 1-dimensional prob- lems. This is a 2-dimensional problem, but the idea (and the update law) remains the same: Ax(i) = -?²ƒ(x(i))-¹?ƒ(x(i))T. We call ?²ƒ(x) the "Hessian" of function f at x, and V² f(x)-¹ is the inverse of the Hessian. Additional note: If you do not know what a notation means, that does not mean make something up and hope you guessed correctly. You have access to nearly all of human knowledge ("the Google"). Use it! Instructor's note, supplemental: You were given a pretty phat tip in class about doing this.