Question

Consider the following nonlinear program:

min

s.t. $-\infty < x< \infty ,$    -$-\infty < y< \infty .$

(a) Express the objective function of the above problem in the standard quadratic function

form:

  $f(x)=\frac{1}{2}x^{T}Qx+c^{T}x$

(b) Find the gradient and the Hessian of f(x).

(c) If possible, solve the minimisation problem and give reasons why the solution you found is a global minimum rather than just a local minimum. Otherwise, demonstrate that the problem is unbounded.

f (x: y) = (x + 2y)2-2x-y

Answer 1

2 2 Hessian matix H is

Hence ね-proHom β unbound ol