Past exam of the numerical linear algebra and continuous optimisation course of the University of Oxford / 2010 / B / 6 / iv / Solution

The Jacobian matrix of $F_{\mu }$ in $(x,y)$ isThe top-left block is the Hessian matrix of $f-y^{T}c$ with $y$ held fixed. In the second block, differentiating $C(x)y$ in $x$ gives $YA$ and in $y$ gives $C$. The explicit derivative with respect to $\mu$ is $(0,-e{)}^T$. Differentiate $F_{\mu }(v(\mu ))=0$ by the chain rule:All blocks are evaluated on the current central path point.