Problem Consider the following optimization problem: min f(x, y) = 3x² + y² x,y (a). Apply one iteration of the gradient descent algorithm with (1, -2) as the initial point and with the parameters a = 0.1 and 3 = 0.5 (b) Apply one iteration of Newton descent algorithm with the same initial point and stepsize selected using backtracking line search. How does the f- value of the new iterate compare to that in (a). How about the amount of work involved in finding the new iterate.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Problem Consider the following optimization problem:
min f(x, y) = 3x² + y*
(a). Apply one iteration of the gradient descent algorithm with (1, –2) as the initial point
and with the parameters a = 0.1 and B = 0.5
(b) Apply one iteration of Newton descent algorithm with the same initial point and stepsize
selected using backtracking line search. How does the f- value of the new iterate compare
to that in (a). How about the amount of work involved in finding the new iterate.
Transcribed Image Text:Problem Consider the following optimization problem: min f(x, y) = 3x² + y* (a). Apply one iteration of the gradient descent algorithm with (1, –2) as the initial point and with the parameters a = 0.1 and B = 0.5 (b) Apply one iteration of Newton descent algorithm with the same initial point and stepsize selected using backtracking line search. How does the f- value of the new iterate compare to that in (a). How about the amount of work involved in finding the new iterate.
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