Let $M=AQ^{-1}A^T$. Since $\nabla h(z)=b-Mz$, <projected gradient descent>[projected gradient ascent] on the nonnegative orthant is
$$
\boxed{z_{k+1}=\bigl[z_k+\eta(b-Mz_k)\bigr]_+,}
$$
where the positive part is componentwise and one may take $0<\eta\leq1/L$.

Solution

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

 Solution

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