Which computer based optimization technique would you recommend for each of the

Question

Which computer based optimization technique would you recommend for each of the following objective functions? Please justify answer briefly in each case. a Powells quartic function: f(x) = (x_1 + 10x_2)^2 + 5 (x_3 - x_4)^2 + (x_2 - 2x_3)^4 + 10 (x_1 - x_4)^4; x^0 = [3, -1, 0, 1]^T;x* = [0, 0, 0, 0]^T b) Fletcher and Powells helical valley; f(x) = 100 ((x_3 - 10 theta (x_1, x_2))^2 + (Squareroot^2_1 + x^2_2 - 1)^2) + x^2_3; where 2 pi theta (x_1, x_2) = {arctan x^2_x_1 if x_1 > 0 pi + arctan x_2/x_1 if x_1

Explanation / Answer

a)

We can use the "active set method" as the optimization technique. this method is very important in

optimization technique because it usually determine the constrain that effect the end result. Its a type of linear programming problem, so we an use "active set method" here.

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