Shapley–Folkman lemma
Okay, so the Shapley-Folkman Lemma is a big fancy idea about how to share things fairly between people. Imagine you have toys, and you want to share them with your friends. But you want to make sure that everyone gets a fair amount of toys.
The Shapley-Folkman Lemma helps you figure out how to do that by breaking up the toys into smaller parts and making sure each part is shared fairly.
So, let's say you have five toys and five friends. One way to share them fairly is to give one toy to each friend. But what if one toy is worth more than another? That's where the Shapley-Folkman Lemma comes in.
It says that you can break up the toys into smaller parts, like two halves or three pieces. Then each friend gets a chance to choose which part they want, and you keep doing that until all the toys are gone. By doing this, everyone gets a fair share of the toys, even if some are worth more than others.
So, to sum it up, the Shapley-Folkman Lemma is a way of sharing things fairly by breaking them up into smaller parts and letting everyone choose which part they want.
The Shapley-Folkman Lemma helps you figure out how to do that by breaking up the toys into smaller parts and making sure each part is shared fairly.
So, let's say you have five toys and five friends. One way to share them fairly is to give one toy to each friend. But what if one toy is worth more than another? That's where the Shapley-Folkman Lemma comes in.
It says that you can break up the toys into smaller parts, like two halves or three pieces. Then each friend gets a chance to choose which part they want, and you keep doing that until all the toys are gone. By doing this, everyone gets a fair share of the toys, even if some are worth more than others.
So, to sum it up, the Shapley-Folkman Lemma is a way of sharing things fairly by breaking them up into smaller parts and letting everyone choose which part they want.