Convex-Optimisation

a linearly separable dataset admits infinitely many separating hyperplanes, and the perceptron will happily hand you whichever one it trips over first. 𐃏 the support vector machine asks a better question: of all the hyperplanes that separate the data, which one is farthest from everybody? the answer — the maximum-margin hyperplane — is determined by a handful of boundary points (the support vectors), drops out of a beautiful convex dual, and generalises via the kernel trick from lines to nearly anything.

As is tradition, the prize pool has increased (to $300 this year).

I have collapsed first and second place into a winner-takes-all arrangement (c’est la vie).

Furthermore, there are additional changes to the structure of this Game:

1. you must now pass the problem set to be awarded the prize money;
2. you may submit your solutions to the problem set at any point in the future;
3. if you plagiarise work, I reserve the right to ban you from all subsequent competitions — grim trigger
4. the problem and solution set will now be courteously supported by MathJaX, TikZ, and my own JavaScript
   • the problems can be found here, whilst the PDF can be found here and here (embedded).
   • my solutions will be available from the start of 2026; by viewing them you forfeit the prize money
5. Good luck!

PDF#

Links#

• Submission link
• List of Past Winners

Structure#

Most notably, the structure from this year has changed. Instead of just offering a single PDF and then writing up solutions on this site, the problems themselves are accessible from below and once 2025 transpires, my solutions will be available as toggled nested environments.