 2023

Solutions to all three questions of the optimisation for data science course of the University of Oxford Part B examination, sat on 7 June 2023. Source: original released PDF, bundle pages 300–303; paper pages 1–4. The original question numbering is retained without reproducing the question statements. Two printing errors on paper page 3 are addressed explicitly in parts 2(c) and 2(f).

Unless a subscript indicates the L1 norm, $\Vert \cdot \Vert$ denotes the Euclidean norm. In Question 1, the regularization weight is $\lambda \ge 0$ and the step size is positive. The big O notation in part 1(d) is interpreted for fixed $x$ as the step size tends to zero, with the necessary subdifferential qualification explained there.