Past exam of the mathematics course of the University of Cambridge / 2023 / iii / Paper 218 / 5 / b / Solution

For coordinate $j$, hold all other coefficients fixed and form the partial residualThe one-coordinate coordinate descent problem isIts exact update isCyclically update coordinates and their residuals until the objective or coefficients converge. Convexity makes every limit point a global minimizer, and ${\lambda }_2>0$ makes it the unique minimizer.