5. Consider a equality constrained optimization problem of the form, min f(x) s.t. g(x) = 0. (9) Here f : R" - R and g : R" - Rm are both twice differentiable and the Lagrangian multiplier of constraint g(x) =0 is defined by A E Rm . 1) Construct the framework of applying Newton's method to solve the problem (9). (10 points) 2) Suppose that the proposed algorithm in 1) is initialized at (x, 10) and with step size 1 convergence to (a*, A*), then, for any invertible matrix A E Rx", prove or disprove applying the proposed algorithm in 1) with step size 1 to problem min f(Au) s.t. g(Au) =0, u with initial points (A la, 10) convergences to (A la*, A*). (10 points)