P3.5 Consider the unconstrained problem m n minimize_(x) = [log (1 ax) - [log...

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P3.5 Consider the unconstrained problem m n minimize_ƒ(x) = − [log (1 − a²x) - [log (1 – x²) i=1 i=1 with variable x € R", and dom ƒ = {x | a{x < 1, i = 1, .…., m, |xi| < 1, i = 1,….., n}. Implement the gradient method and Newton's method with backtracking line search to estimate the solution of the above problem. • Use m = 200 and n = 100 and generate data according to: m=200; n=100; randn ('seed', 319) ; A= randn (m, n); The data af are the rows of the generated matrix A. • Use initialization (0) = 0 and line search parameters: Terminate the algorithm if ||Vf(x))|| < 10−4. = 1/2, and y = 0.01. Turn in the code for your solution. For both algorithms, write down the number of iterations T needed until the stopping criteria is met. Hint. Use the composition with affine function property to find an expression for the gradient and Hessian, which can be computed in MATLAB. At each iteration, ensure that the stepsize ao is small enough so that the next iterate is in the domain of f. P3.5 Consider the unconstrained problem m n minimize_ƒ(x) = − [log (1 − a²x) - [log (1 – x²) i=1 i=1 with variable x € R", and dom ƒ = {x | a{x < 1, i = 1, .…., m, |xi| < 1, i = 1,….., n}. Implement the gradient method and Newton's method with backtracking line search to estimate the solution of the above problem. • Use m = 200 and n = 100 and generate data according to: m=200; n=100; randn ('seed', 319) ; A= randn (m, n); The data af are the rows of the generated matrix A. • Use initialization (0) = 0 and line search parameters: Terminate the algorithm if ||Vf(x))|| < 10−4. = 1/2, and y = 0.01. Turn in the code for your solution. For both algorithms, write down the number of iterations T needed until the stopping criteria is met. Hint. Use the composition with affine function property to find an expression for the gradient and Hessian, which can be computed in MATLAB. At each iteration, ensure that the stepsize ao is small enough so that the next iterate is in the domain of f.

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Explanation The code aims to find the minimum value of a specific mathematical function using two methods the Gradient Method and Newtons Method It starts with a guess and continuously changes it unti... View the full answer