 Solution

ID: past-exam-of-the-numerical-linear-algebra-and-continuous-optimisation-course-of-the-university-of-oxford/2010/b/6/iv/solution

F_{μ}

(x, y)

J (v) = (H (x, y) Y A (x) - A (x)^{T} C (x)) .

The top-left block is the Hessian matrix of

f - y^{T} c

with

y

held fixed. In the second block, differentiating

C (x) y

x

gives

Y A

and in

y

gives

C

. The explicit derivative with respect to

μ

(0, - e)^{T}

. Differentiate

F_{μ} (v (μ)) = 0

(H Y A - A^{T} C) (x^{'} (μ) y^{'} (μ)) = (0 e) .

All blocks are evaluated on the current central path point.

 New to topics? Read the docs here!