1. [25 marks| Consider minimizing the strictly convex quadratic function glx) = -;-:'Gx+d"x+c where G is an (n X n) symmetric positive definite constant matrix, d is a constant n x 1 vector and c is a scalar. Let x*) be the starting point, where Vg(x{") 0, xM % x* and x* is the minimizer of g(x). i) Consider applying the descent method with exact line searches to the steepest quadratic function g(x). Let {x*}2, be the sequence generated by the steepest descent method with exact line searches. a) Write down the steepest descent direction s}' at x. b) Confirm that s} is a descent direction. ) Write down the line search condition that must be satisfied by the exact minimizer a of (a) = g(x* + as}'). d) Hence or otherwise show that (x(** x(B+1))T(x(k+1) _ &) = @