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

Let $M=A{Q}^{-1}{A}^T$. Since $\nabla h(z)=b-Mz$, projected gradient ascent on the nonnegative orthant iswhere the positive part is componentwise and one may take $0<\eta \le 1/L$.