Consider Newton's method applied to the minimisation problemminxf(x).min𝑥𝑓(𝑥).Which of the following statements is true regarding the convergence of Newton's method.Question 1Answera.If f𝑓 is convex and has positive definite Hessian for all x𝑥 and Newton's method converges, then it converges to a global minimiser of f𝑓.b.Newton's method always converges to a global minimiser of f𝑓. c.If f𝑓 is convex and has positive definite Hessian for all x𝑥 then Newton's method always converges.d.Newton's method always requires damping in order to converge to a global minimiser of f𝑓.

Gradient Descent algorithms converge to a local minimum, and if the function is convex, they converge to a __________ minimum.

Which of the following statements about coordinate descent is true? (Select all that apply.)Group of answer choicesTo test the convergence of coordinate descent, look at the size of the maximum step you take as you cycle through coordinates.Coordinate descent cannot be used to optimize the ordinary least squares objective.Coordinate descent is always less efficient than gradient descent, but is often easier to implement.A small enough step size should be chosen to guarantee convergence.

Which of the following statements about Gradient Descent are true? (Select all that apply)Group of answer choicesLearning rate is a crucial hyperparameter in its performance.It requires calculation of gradients for the entire dataset.It can be very slow when the dataset is very large.It is guaranteed to find the global minimum for non-convex functions.

41.What does gradient descent help in finding?  A. Local maximum of a function  B. Local minimum of a function  C. Global maximum of function  D. Global minimum of function

In Newton Raphson method, if the curve 𝑓(𝑥)f(x) is constant then ________.a)None of the mentionedb)𝑓′(𝑥)=0f ′ (x)=0c)𝑓(𝑥)=0f(x)=0d)𝑓′(𝑥)=𝑐f ′ (x)=c