Homework SourseConsider minimization of the following function fx y x2 3y
Consider minimization of the following function. f(x, y) = x^2 + 3(y-l)^4. starting from (x, y) = [1 2]T. Explain briefly how to generate two mutually conjugate search directions by evaluating f(X) only (without using gradient vectors). Perform 2 iterations of conjugate gradient method (also known as Fletcher-Reeves method) to minimize the above function.![Consider minimization of the following function. f(x, y) = x^2 + 3(y-l)^4. starting from (x, y) = [1 2]T. Explain briefly how to generate two mutually conjugat](/WebImages/29/consider-minimization-of-the-following-function-fx-y-x2-3y-1082501-1761568696-0.webp "Consider minimization of the following function. f(x, y) = x^2 + 3(y-l)^4. starting from (x, y) = [1 2]T. Explain briefly how to generate two mutually conjugat")
Solution
a) f(1,2) = 4
f(X) = d (f(x,y))/dx = 2x
b) xn+1 = xn - f(xn)/f\'(xn)
n = 1 x=2
n=2 x=3
