3. Write a function in Matlab or other suitable programming language to im- plement Newton's method for optimization, using the Armijo/backtracking line search and switching to steepest descent (dk -Vf(x)) if the Hessian matrix Hess f(xk) is not positive definite. Whenever we use the Newton step (dk[Hess,f(x)-' f(x)) we use the initial step length parame- ter 00 1 in the line search. Apply this to the function in HWI Q1 with various starting points including several close to the saddle point. Report numbers of function, gradient and Hessian matrix evaluations, and the gra- dient of the objective function at the end. [Note: It is good programming practice to have the function or functions for the f and its gradient and Hes- sian matrix to be separate from the code implementing Newton's method. This way, the function etc. can be tested independently of the optimization method.] 3. Write a function in Matlab or other suitable programming language to im- plement Newton's method for optimization, using the Armijo/backtracking line search and switching to steepest descent (dk -Vf(x)) if the Hessian matrix Hess f(xk) is not positive definite. Whenever we use the Newton step (dk[Hess,f(x)-' f(x)) we use the initial step length parame- ter 00 1 in the line search. Apply this to the function in HWI Q1 with various starting points including several close to the saddle point. Report numbers of function, gradient and Hessian matrix evaluations, and the gra- dient of the objective function at the end. [Note: It is good programming practice to have the function or functions for the f and its gradient and Hes- sian matrix to be separate from the code implementing Newton's method. This way, the function etc. can be tested independently of the optimization method.]