Return to the unconstrained optimization of Exercise 16-31 and consider BFGS Algorithm 16F starting at x102 = 12, 32.

(a) Compute the first direction that would be pursued by Algorithm 16F.

(b) Assuming that the optimal step is l =

0.026 in that direction, compute the new solution x112, the next deflection matrix D, and the next BFGS search direction x.

(c) Verify that your deflection matrix of part

(b) satisfies quasi-Newton conditions 16.43

(within roundoff error) and is symmetric.

(d) Verify algebraically that your direction of part

(b) is improving.

(e) Plot your first move and second direction on a contour map like that of Exercise 16-31(a).