Fenchel's duality theorem

Fenchel's duality theorem is like a secret code that helps us unlock a way to solve certain math problems. Imagine you have two friends who both like to play games, but they have different games they like to play. One friend likes to play baseball, while the other likes to play soccer.

Now, let's say you want to have a big tournament with both baseball and soccer games. You could try to figure out a way to combine the two games, but that might be really hard. Instead, Fenchel's duality theorem lets you create a secret code that lets you switch between playing baseball and playing soccer, without having to mix the two games together.

In math terms, Fenchel's duality theorem relates two different problems, just like baseball and soccer are two different games. It allows us to switch between the problems, without having to combine them into one big problem. This makes it easier to solve them both, and even compare their solutions to see which one is better.

So, if you ever come across a math problem that seems really hard to solve, remember Fenchel's duality theorem. It's like a secret code that helps you switch between different problems and find the best solution for each one.