Unit 5

Question 1

What are the table headers for the Newton updating formula (L->R)?

Answer 1

Iteration
x(t)
F(x(t))
F’(x(t))
h(t)

Question 2

How do you know when you have reached the value where F(x)=0 when doing newton updating formula?

Answer 2

When x and F’(x) converge to values, and F(x) and h converge to 0

Question 3

What was the rosenbrock test function?

Answer 3

It was a function designed to test the performance of optimisation algorithms

f(x1,x2)=M(x2-x1^2)+(1-x1)^2 M=1000

UGMin at (1,1)

Question 4

Explain the first difficulty with numerical unconstrained optimisation?

Answer 4

No guarantee with the NR algorithm that f(x(t+1)) will actually be smaller than f(x(t)). HOWEVER can be sure that the search direction is an improvement direction provided H(x(t)) is positive definite (see notes)

Question 5

Explain the second difficulty with numerical unconstrained optimisation?

Answer 5

Hessian matrix may be laborious to compute - so called quasi-Newton algorithms get round this problem (see notes)