7. Use the gradient-based optimization algorithm (grad_opt1) to find the minima of the function f(x) = cos(ex) + x² - 1.

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7 Use The Gradient Based Optimization Algorithm Grad Opt1 To Find The Minima Of The Function F X Cos Ex X 1 1 (58.42 KiB) Viewed 21 times

7. 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? 8. Repeat Problem 7 using grad_opt2. Which method is more reliable, grad_opt2 or grad_opt1? Explain.