代做CHE 431留学生、代写MATLAB程序语言、代做MATLAB代写、代写BlackBoard-代写Matlab编程

CHE 431, Spring 2019, Problem Set 6

Due date: 11:59pm, Tue, 03/12/2019.

Problem 1 (10 pts). Let f(~x) = (1.5 x1 + x1x2)

, where ~x = (x1, x2).

Write a MATLAB script to find the minimum of f(~x) using ”Dogleg Trust

Region” method and the following steps:

Set the condition for global convergence: ||~ f(~x)|| < T ol, where T ol

Consider ρ = (f(~x) f(~x + ~p))/(m(~x,~0) m(~x, ~p)), where ~p is the

chosen direction (which is NOT normalized) at every iteration,

m(~x, ~p) = f(~x) +~ f(~x).~p + 1/2 ~p B ~p,

and B is the Hessian matrix. Then

if ρ < η1, set = t1

elseif (ρ > η2 and |||~p|| < 0.001) set = min(t2, max)

end

where η1 = 0.25, η2 = 0.75, t1 = 0.25, t2 = 2, and max = 5.

Initialize = 2.

Set the initial guess to ~x0 = (3, 2), and maximum number of iterations

to 50.

For each iteration, your script should print out the following (numerical

values are shown as an example of such print-out):

Iter= 1; ~x=[ 2.827, 1.627]; ~p=[-0.173,-0.373];= 5.0000e-01; ρ= 1.245;

λ= 0.190

where λ = ( ||~pS||)/||~pN ~pS||), and ~pN and ~pS are Newton’s and

steepest descent direction vectors (which are NOT normalized), respectively.

Submit the MATLAB script on BlackBoard.

Hint: An image of the convergence path is shown below.