please use Python or Matlab to show all the work

3. (30 points) Consider minimizing the function f=(x - 1)2 + (2 y-1 ) by constant step size steepest descent method. a) Find a step size a, to satisfy Wolfe conditions (for any initial point) with c =1/6, C2=2/3. b) Initialize at point (4, 1), use step length a, to compute || X k+1 - x* || / || Xk-x* || when norm (D f) = 10 -9. c) Write the function f into the form 72 x"Q x -b? x + 2, compute eigenvalues 2 max (Q), 2 min (Q) , step size Q2 = 2/ ( a max (Q)+ 2 min (Q)), and constant r= (a (Q) - 2 min (Q))/(a max (Q)+2 min (Q)). max d) Repeat b) for step size Q2 . How close are the outputs of b) and d) to r ? 3. (30 points) Consider minimizing the function f=(x - 1)2 + (2 y-1 ) by constant step size steepest descent method. a) Find a step size a, to satisfy Wolfe conditions (for any initial point) with c =1/6, C2=2/3. b) Initialize at point (4, 1), use step length a, to compute || X k+1 - x* || / || Xk-x* || when norm (D f) = 10 -9. c) Write the function f into the form 72 x"Q x -b? x + 2, compute eigenvalues 2 max (Q), 2 min (Q) , step size Q2 = 2/ ( a max (Q)+ 2 min (Q)), and constant r= (a (Q) - 2 min (Q))/(a max (Q)+2 min (Q)). max d) Repeat b) for step size Q2 . How close are the outputs of b) and d) to r