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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.

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
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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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