Consider the problem -

min f(x) = 2x12 +3x2 −3x1x2 +2x1 −4x2

Starting from the initial point x1 = 0, x2 = 0 solve the problem using two methods -

• Davidon-Fletcher-Powell (DFP) Method
• Fletcher-Reeves (FR) Conjugate Gradient method

The first method corresponds to a Quasi-Newton method which is to be implemented with the initial approximation of the inverse of the hessian as identity : D1 = I2. Further show that the directions generated by the two methods at every iteration are identical and explain the reason behind this.