Homework 4 Solution

Exercise 5 from Chapter 3 of the Draft notes (about short steps).



Exercise 9 from Chapter 3 of the Draft notes (about regularized least squares).



Exercise 5.2 from Numerical Optimization, 2nd Ed .



Exercise 5.7 from Numerical Optimization, 2nd Ed .



For the quadratic function of Section 4.6 in the Draft notes, prove the following bounds:







(n k)3


(n k)3
kx0 x k22 n=3; kxk
x k2






kx0 x k2:
3(n + 1)2
n(n + 1)2



(The bound (4.40) in the Draft notes follows by setting k = this expression and noting that it is decreasing in k.)







n
1 in
2




















































































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