What is a rank-two update in numerical optimization, and why is the BFGS algorithm considered an example of such an update?
A) A rank-two update involves modifying a matrix by adding a matrix of rank 2 to it, enhancing its performance. The BFGS algorithm achieves this by updating the Hessian matrix.
B) A rank-two update involves reducing the rank of a matrix by 2, making it less complex. The BFGS algorithm accomplishes this by simplifying the Hessian matrix.
C) A rank-two update refers to the process of adjusting a matrix using two separate rank-one updates. The BFGS algorithm employs two separate updates to enhance the Hessian matrix.
D) A rank-two update is a technique used in gradient descent optimization. The BFGS algorithm, as an iterative optimization method, leverages this update to efficiently converge to the optimal solution.
