Use the gradient-based optimization algorithm (grad_opt1) to find the minima of the function f(x) = cos(ex) + x²-1. Employ a rate parameter of -0.02 and -0.001, and start from initial search points in the set (1.5, 2.5, 3). Set TOL=10^-6 and IMAX=1000. For each case, generate a plot for the evolution of the search point x value vs iteration 't' (six plots total). Compare your results to the true minima shown in the plot of f(x) within the interval [04]. Does the method always lead to the minimum closest to the initial search point?
Use the gradient-based optimization algorithm (grad_opt1) to find the minima of the function f(x) = cos(ex) + x²-1. Employ a rate parameter of -0.02 and -0.001, and start from initial search points in the set (1.5, 2.5, 3). Set TOL=10^-6 and IMAX=1000. For each case, generate a plot for the evolution of the search point x value vs iteration 't' (six plots total). Compare your results to the true minima shown in the plot of f(x) within the interval [04]. Does the method always lead to the minimum closest to the initial search point?
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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![Advanced Physics
7. Use the gradient-based optimization algorithm (grad_opt1) to find the minima of the
function f(x) = cos(er) + x²-1. Employ a rate parameter of -0.02 and -0.001, and start
from initial search points in the set (1.5, 2.5, 3). Set TOL=10^-6 and IMAX=1000. For each
case, generate a plot for the evolution of the search point x value vs iteration 't' (six plots
total). Compare your results to the true minima shown in the plot of f(x) within the interval
[04]. Does the method always lead to the minimum closest to the initial search point?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F450cfc39-a0b3-41ad-b01f-57c67b514b9d%2F0df92841-4dfc-4bd6-9fa2-be14f4317209%2Fyhd7gp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Advanced Physics
7. Use the gradient-based optimization algorithm (grad_opt1) to find the minima of the
function f(x) = cos(er) + x²-1. Employ a rate parameter of -0.02 and -0.001, and start
from initial search points in the set (1.5, 2.5, 3). Set TOL=10^-6 and IMAX=1000. For each
case, generate a plot for the evolution of the search point x value vs iteration 't' (six plots
total). Compare your results to the true minima shown in the plot of f(x) within the interval
[04]. Does the method always lead to the minimum closest to the initial search point?
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