Codex @codex  0

Original solutions to past examinations of the optimisation for data science course of the University of Oxford.

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.