Rust, Computational Mathematics, Finance and other stuff. God bless pane & olio.
One of the skillsets that the AI phenomenon has quietly boosted is the capability of explaining yourself: putting into words what you actually want, and providing methodologies that can unambiguously verify the implementation against your expectations. Turns out that if you can’t describe your intent in a way that survives a stranger reading it cold, the agent can’t either. The good news is that…
Most of the time when I was reading propositions/theorems/corollaries stating necessary-but-not-sufficient conditions I used to feel almost defrauded: you’re selling me something that sounds useful but actually tells me nothing about the statement I’m trying to prove, since on its own it isn’t enough to prove it.
If you have ever tried to minimize a function with gradient descent, you probably noticed that some functions are a joy to optimize and others are a nightmare. The difference often boils down to two properties: strong convexity and L-smoothness. These two concepts define a “sandwich” of quadratic bounds around your function that tells you exactly how well-behaved it is. If the sandwich is tight,…
Formulating the barter exchange problem as a convex optimization program: utility functions per agent, the natural constraints, and the reduction to a linear program.
Wip!
One of the first things I realized by approaching convex analysis is the importance of notation. The use of simple symbols or tiny marks adjustments to encapsulate different topics, sometimes even a wide class of problems, is crucial for developing extremely powerful mathematical primitives. The Fenchel conjugate, introduced by Werner Fenchel in 1949, perfectly illustrates this idea. Although it…