We need to prove that when we apply the Newton-Raphson method to strictly quadratic concave function. It will converge in one step.How to apply this method to maximization of f ( x ) = 4 ⋅ x 1 + 6 ⋅ x 2 − 2 ⋅ x 1 2 − 2 ⋅ x 1 ⋅ x 2 − 2 ⋅ x 2 2 I did not understand how to apply method to this function? what should be the interval?

Question

We need to prove that when we apply the Newton-Raphson method to strictly quadratic concave function. It will converge in one step.How to apply this method to maximization of  f  (  x  )  =  4  ⋅      x    1    +  6  ⋅      x    2    −  2  ⋅      x    1    2    −  2  ⋅      x    1    ⋅      x    2    −  2  ⋅      x    2    2  I did not understand how to apply method to this function? what should be the interval?

Freddy Doyle · Accepted Answer

You don&#039;t need an interval. You are using Newton-Raphson to find a solution of the system                                                        ∂              f                                      ∂                              x                1                                                                =        4        −        4                  x          1                −        2                  x          2                =        0                                                                ∂              f                                      ∂                              x                2                                                                =        6        −        2                  x          1                −        4                  x          2                =        0            This being a linear system, it doesn&#039;t matter where your initial point is: Newton-Raphson simply solves the linear system.