HW 4

Optimization Methods Fall 2001

October 5, 2011

1. Search for a minimum of a function

f(x) = (x_{1} − x_{2}^{2})^{2} + (1 − x_{1})^{2} + x_{2}x_{3} + 3 x_{3}^{4}, x_{0} = [0, 1, 1]

by

a) Conjugate gradient method (any variant)

b) Quasinewton method (any variant)

Show the history of iterations, compare

2. 5.8 (Take n=8, diagonal matrices, eigenvalues are a) 1, 2, 3, 3, 3, 5, 5, 8.

b) 1,2,3, 4, 5, 6, 7, 8.

3. 5.11

4. 6.2

5. 6.4

6. Bonus 6.10