The Hessian of $-h$ is $M=AQ^{-1}A^T$. Thus $-h$ is strongly convex exactly when $A$ has <full row rank>. In that case one may use
$$
\boxed{\mu\geq\frac{\lambda_{\min}(AA^T)}{\lambda_{\max}(Q)}.}
$$
In all cases, the gradient has Lipschitz constant bounded by
$$
\boxed{L=\lambda_{\max}(M)
\leq\frac{\|A\|_2^2}{\lambda_{\min}(Q)}.}
$$

Solution

Past exam of the mathematics course of the University of Cambridge / 2022 / iii / Paper 339 / 2 / c / ii / Solution

 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2022/iii/paper-339/2/c/ii/solution